Problem 834

Add and Divide - U(1234567). Pure Flow port of the native C solver.

Answer1254404167198752370
Output1254404167198752370
StatusPASS
Native helperno
Runtime220 ms
Peak memory7088 KB
Time complexityO(n^2) (estimated)
Space complexityO(n^2) (estimated)

Performance comparison

MetricOur solutionBest known
Time complexityO(n^2)?
Space complexityO(n^2)?
ApproachFlow solutionNot curated
VerdictUnknown

Flow source

# Project Euler 834
# Add and Divide - U(1234567).
# Pure Flow port of the native C solver.

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
    function malloc(n: i64) -> ptr<void>
}

const N_LIMIT: i32 = 1234567

# Global SPF array
let mut g_spf: ptr<i32> = null
let mut g_cnt: i64 = 0
let mut g_sum: i64 = 0

function build_spf(limit: i32) -> void {
    g_spf = calloc((limit as i64) + 1, 4)
    let primes: ptr<i32> = malloc(((limit as i64) + 1) * 4)
    let mut pcnt: i32 = 0
    let mut i: i32 = 2
    while i <= limit {
        if g_spf[i] == 0 {
            g_spf[i] = i
            primes[pcnt] = i
            pcnt = pcnt + 1
        }
        let mut j: i32 = 0
        while j < pcnt {
            let ip: i32 = i * primes[j]
            if ip > limit { break }
            g_spf[ip] = primes[j]
            if primes[j] == g_spf[i] { break }
            j = j + 1
        }
        i = i + 1
    }
    free(primes)
    g_spf[0] = 0
    if limit >= 1 { g_spf[1] = 1 }
}

# Divisor data: sorted divisors, prefix sums, total sum
struct DivData {
    divs: ptr<i32>
    pre: ptr<i64>
    count: i32
    total: i64
}

function insertion_sort(arr: ptr<i32>, n: i32) -> void {
    let mut i: i32 = 1
    while i < n {
        let key: i32 = arr[i]
        let mut j: i32 = i - 1
        while j >= 0 {
            if arr[j] > key {
                arr[j + 1] = arr[j]
                j = j - 1
            } else {
                break
            }
        }
        arr[j + 1] = key
        i = i + 1
    }
}

function divisors_with_prefix(odd_x: i32) -> DivData {
    if odd_x == 1 {
        let divs: ptr<i32> = malloc(4)
        divs[0] = 1
        let pre: ptr<i64> = malloc(16)
        pre[0] = 0
        pre[1] = 1
        return DivData { divs: divs, pre: pre, count: 1, total: 1 }
    }

    # Factorize using SPF
    let factors_p: ptr<i32> = malloc(256)
    let factors_e: ptr<i32> = malloc(256)
    let mut nfac: i32 = 0
    let mut x: i32 = odd_x
    while x > 1 {
        let p: i32 = g_spf[x]
        let mut e: i32 = 0
        while x % p == 0 {
            x = x / p
            e = e + 1
        }
        factors_p[nfac] = p
        factors_e[nfac] = e
        nfac = nfac + 1
    }

    # Generate divisors
    let mut cap: i32 = 1
    let mut i: i32 = 0
    while i < nfac {
        cap = cap * (factors_e[i] + 1)
        i = i + 1
    }
    let divs: ptr<i32> = malloc((cap as i64) * 4)
    let mut ndiv: i32 = 1
    divs[0] = 1
    let mut i2: i32 = 0
    while i2 < nfac {
        let p: i32 = factors_p[i2]
        let e: i32 = factors_e[i2]
        let base_ndiv: i32 = ndiv
        let mut mult: i32 = 1
        let mut k: i32 = 1
        while k <= e {
            mult = mult * p
            let mut j: i32 = 0
            while j < base_ndiv {
                divs[ndiv] = divs[j] * mult
                ndiv = ndiv + 1
                j = j + 1
            }
            k = k + 1
        }
        i2 = i2 + 1
    }

    insertion_sort(divs, ndiv)

    let pre: ptr<i64> = malloc(((ndiv as i64) + 1) * 8)
    let mut s: i64 = 0
    let mut i3: i32 = 0
    while i3 < ndiv {
        s = s + (divs[i3] as i64)
        pre[i3 + 1] = s
        i3 = i3 + 1
    }

    free(factors_p)
    free(factors_e)
    return DivData { divs: divs, pre: pre, count: ndiv, total: s }
}

# Binary search: rightmost index where divs[idx] <= bound
function bisect_right(divs: ptr<i32>, count: i32, bound: i32) -> i32 {
    let mut lo: i32 = 0
    let mut hi: i32 = count
    while lo < hi {
        let mid: i32 = (lo + hi) / 2
        if divs[mid] <= bound {
            lo = mid + 1
        } else {
            hi = mid
        }
    }
    return lo
}

# Over pairs (a in small, b in large), count and sum where a*b > bound
# Results stored in g_cnt and g_sum
function count_sum_products_gt(
    small: ptr<i32>, ns: i32, large: ptr<i32>, nl: i32,
    lpre: ptr<i64>, ltotal: i64,
    bound: i32) -> void {
    g_cnt = 0
    g_sum = 0
    let mut i: i32 = 0
    while i < ns {
        let a: i32 = small[i]
        let idx: i32 = bisect_right(large, nl, bound / a)
        if idx != nl {
            g_cnt = g_cnt + (nl - idx) as i64
            g_sum = g_sum + (a as i64) * (ltotal - lpre[idx])
        }
        i = i + 1
    }
}

function compute_T(n: i64, two: i32, dA: DivData, dB: DivData) -> i64 {
    let mut small: ptr<i32> = null
    let mut large: ptr<i32> = null
    let mut ns: i32 = 0
    let mut nl: i32 = 0
    let mut preL: ptr<i64> = null
    let mut sumL: i64 = 0

    if dA.count <= dB.count {
        small = dA.divs; ns = dA.count
        large = dB.divs; nl = dB.count
        preL = dB.pre; sumL = dB.total
    } else {
        small = dB.divs; ns = dB.count
        large = dA.divs; nl = dA.count
        preL = dA.pre; sumL = dA.total
    }

    let n_i32: i32 = n as i32
    let bound1: i32 = n_i32
    let bound2: i32 = n_i32 / two

    count_sum_products_gt(small, ns, large, nl, preL, sumL, bound1)
    let cnt1: i64 = g_cnt
    let sum1: i64 = g_sum
    count_sum_products_gt(small, ns, large, nl, preL, sumL, bound2)
    let cnt2: i64 = g_cnt
    let sum2: i64 = g_sum

    let count_total: i64 = cnt1 + cnt2
    let sum_d: i64 = sum1 + (two as i64) * sum2
    return sum_d - n * count_total
}

function main() -> i32 {
    let N: i32 = N_LIMIT
    build_spf(N)

    let mut total: i64 = 0
    let mut lastA: i32 = -1
    let mut lastB: i32 = -1
    let mut dataA: DivData = DivData { divs: null, pre: null, count: 0, total: 0 }
    let mut dataB: DivData = DivData { divs: null, pre: null, count: 0, total: 0 }

    let mut n: i32 = 3
    while n <= N {
        let even: i32
        let B: i32
        if (n & 1) != 0 {
            even = n - 1
            B = n
        } else {
            even = n
            B = n - 1
        }

        # odd part and 2^v2
        let two: i32 = even & (0 - even)
        let A: i32 = even / two

        if A != lastA {
            if lastA != -1 {
                free(dataA.divs)
                free(dataA.pre)
            }
            dataA = divisors_with_prefix(A)
            lastA = A
        }
        if B != lastB {
            if lastB != -1 {
                free(dataB.divs)
                free(dataB.pre)
            }
            dataB = divisors_with_prefix(B)
            lastB = B
        }

        total = total + compute_T(n as i64, two, dataA, dataB)
        n = n + 1
    }

    free(dataA.divs)
    free(dataA.pre)
    free(dataB.divs)
    free(dataB.pre)
    free(g_spf)

    printf("%lld\n", total)
    return 0
}

Generated C

#include <stdint.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/* Flow runtime helpers */
typedef struct flow_temp_node { struct flow_temp_node* next; } flow_temp_node;
static flow_temp_node* flow_temp_head = NULL;
static int flow_temp_atexit_set = 0;
__attribute__((unused)) static void flow_temp_free_all(void) {
    while (flow_temp_head) {
        flow_temp_node* n = flow_temp_head;
        flow_temp_head = n->next;
        free(n);
    }
}
__attribute__((unused)) static void* flow_temp_alloc(size_t nbytes) {
    flow_temp_node* node = (flow_temp_node*)malloc(sizeof(flow_temp_node) + nbytes);
    if (!node) return NULL;
    node->next = flow_temp_head;
    flow_temp_head = node;
    if (!flow_temp_atexit_set) {
        flow_temp_atexit_set = 1;
        atexit(flow_temp_free_all);
    }
    return (void*)(node + 1);
}
#ifndef FLOW_DIAG
#define FLOW_DIAG(msg) fprintf(stderr, "%s", (msg))
#endif
#ifndef FLOW_LOG
#define FLOW_LOG(fmt, ...) printf(fmt, __VA_ARGS__)
#endif
#ifndef FLOW_LOG_EMPTY
#define FLOW_LOG_EMPTY(fmt) printf(fmt)
#endif
static char* flow_strcat(const char* a, const char* b) {
    size_t la = strlen(a ? a : ""), lb = strlen(b ? b : "");
    char* r = (char*)flow_temp_alloc(la + lb + 1);
    if (!r) return NULL;
    if (la) memcpy(r, a, la);
    if (lb) memcpy(r + la, b, lb);
    r[la + lb] = '\0';
    return r;
}

#define __flow_in_arr(arr, val) __extension__ ({ \
    int _found = 0; \
    size_t _n = sizeof(arr)/sizeof((arr)[0]); \
    for (size_t _i = 0; _i < _n; _i++) { \
        if ((arr)[_i] == (val)) { _found = 1; break; } \
    } _found; })

/* Unified fault handler (MISRA #279) — override with -DFLOW_FAULT_HANDLER=fn */
#ifndef FLOW_FAULT_HANDLER
__attribute__((unused)) static inline void flow_fault_handler(const char* msg) {
    fprintf(stderr, "flow: %s\n", msg ? msg : "fault");
    abort();
#if defined(__GNUC__) || defined(__clang__)
    __builtin_unreachable();
#endif
}
#else
#define flow_fault_handler FLOW_FAULT_HANDLER
#endif
#define flow_div_by_zero_handler() flow_fault_handler("division by zero")
#define flow_shift_ub_handler() flow_fault_handler("invalid shift (amount out of range or left-shift of negative)")

#ifndef FLOW_CHECKED_DIV
#define FLOW_CHECKED_DIV(L, R) (((R) != 0) ? ((L) / (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_MOD
#define FLOW_CHECKED_MOD(L, R) (((R) != 0) ? ((L) % (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHL
#define FLOW_CHECKED_SHL(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull)) && ((L) >= 0)) ? ((L) << (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHR
#define FLOW_CHECKED_SHR(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull))) ? ((L) >> (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif

#include <math.h>

void* _ui_state = NULL;

static inline float i32_to_f32(int32_t v) { return (float)v; }

/* Host stub for @gpu kernels (device codegen replaces this). */
static inline int32_t gpu_thread_id(void) { return 0; }

typedef struct DivData DivData;

struct DivData {
    int32_t* divs;
    int64_t* pre;
    int32_t count;
    int64_t total;
};

void build_spf_i32(int32_t limit);
void insertion_sort_ptr_i32_i32(int32_t* arr, int32_t n);
DivData divisors_with_prefix_i32(int32_t odd_x);
int32_t bisect_right_ptr_i32_i32_i32(int32_t* divs, int32_t count, int32_t bound);
void count_sum_products_gt_ptr_i32_i32_ptr_i32_i32_ptr_i64_i64_i32(int32_t* small, int32_t ns, int32_t* large, int32_t nl, int64_t* lpre, int64_t ltotal, int32_t bound);
int64_t compute_T_i64_i32_DivData_DivData(int64_t n, int32_t two, DivData dA, DivData dB);
int32_t main(void);

static const int32_t N_LIMIT = 1234567;

/* Module statics */
static int32_t* g_spf = NULL;
static int64_t g_cnt = 0;
static int64_t g_sum = 0;




void build_spf_i32(int32_t limit) {
    g_spf = calloc((((int64_t)(limit)) + 1), 4);
    int32_t* primes = (int32_t*)(malloc(((((int64_t)(limit)) + 1) * 4)));
    int32_t pcnt = 0;
    int32_t i = 2;
    while (i <= limit) {
        if (g_spf[i] == 0) {
            g_spf[i] = i;
            primes[pcnt] = i;
            pcnt = (pcnt + 1);
        }
        int32_t j = 0;
        while (j < pcnt) {
            int32_t ip = (i * primes[j]);
            if (ip > limit) {
                break;
            }
            g_spf[ip] = primes[j];
            if (primes[j] == g_spf[i]) {
                break;
            }
            j = (j + 1);
        }
        i = (i + 1);
    }
    free(primes);
    g_spf[0] = 0;
    if (limit >= 1) {
        g_spf[1] = 1;
    }
}

void insertion_sort_ptr_i32_i32(int32_t* arr, int32_t n) {
    int32_t i = 1;
    while (i < n) {
        int32_t key = arr[i];
        int32_t j = (i - 1);
        while (j >= 0) {
            if (arr[j] > key) {
                arr[(j + 1)] = arr[j];
                j = (j - 1);
            } else {
                break;
            }
        }
        arr[(j + 1)] = key;
        i = (i + 1);
    }
}

DivData divisors_with_prefix_i32(int32_t odd_x) {
    if (odd_x == 1) {
        int32_t* divs = (int32_t*)(malloc(4));
        divs[0] = 1;
        int64_t* pre = (int64_t*)(malloc(16));
        pre[0] = 0;
        pre[1] = 1;
        return (DivData){ .divs = divs, .pre = pre, .count = 1, .total = 1 };
    }
    int32_t* factors_p = (int32_t*)(malloc(256));
    int32_t* factors_e = (int32_t*)(malloc(256));
    int32_t nfac = 0;
    int32_t x = odd_x;
    while (x > 1) {
        int32_t p = g_spf[x];
        int32_t e = 0;
        while (FLOW_CHECKED_MOD((x), (p)) == 0) {
            x = FLOW_CHECKED_DIV((x), (p));
            e = (e + 1);
        }
        factors_p[nfac] = p;
        factors_e[nfac] = e;
        nfac = (nfac + 1);
    }
    int32_t cap = 1;
    int32_t i = 0;
    while (i < nfac) {
        cap = (cap * (factors_e[i] + 1));
        i = (i + 1);
    }
    int32_t* divs = (int32_t*)(malloc((((int64_t)(cap)) * 4)));
    int32_t ndiv = 1;
    divs[0] = 1;
    int32_t i2 = 0;
    while (i2 < nfac) {
        int32_t p = factors_p[i2];
        int32_t e = factors_e[i2];
        int32_t base_ndiv = ndiv;
        int32_t mult = 1;
        int32_t k = 1;
        while (k <= e) {
            mult = (mult * p);
            int32_t j = 0;
            while (j < base_ndiv) {
                divs[ndiv] = (divs[j] * mult);
                ndiv = (ndiv + 1);
                j = (j + 1);
            }
            k = (k + 1);
        }
        i2 = (i2 + 1);
    }
    insertion_sort_ptr_i32_i32(divs, ndiv);
    int64_t* pre = (int64_t*)(malloc(((((int64_t)(ndiv)) + 1) * 8)));
    int64_t s = 0;
    int32_t i3 = 0;
    while (i3 < ndiv) {
        s = (s + ((int64_t)(divs[i3])));
        pre[(i3 + 1)] = s;
        i3 = (i3 + 1);
    }
    free(factors_p);
    free(factors_e);
    return (DivData){ .divs = divs, .pre = pre, .count = ndiv, .total = s };
}

int32_t bisect_right_ptr_i32_i32_i32(int32_t* divs, int32_t count, int32_t bound) {
    int32_t lo = 0;
    int32_t hi = count;
    while (lo < hi) {
        int32_t mid = FLOW_CHECKED_DIV(((lo + hi)), (2));
        if (divs[mid] <= bound) {
            lo = (mid + 1);
        } else {
            hi = mid;
        }
    }
    return lo;
}

void count_sum_products_gt_ptr_i32_i32_ptr_i32_i32_ptr_i64_i64_i32(int32_t* small, int32_t ns, int32_t* large, int32_t nl, int64_t* lpre, int64_t ltotal, int32_t bound) {
    g_cnt = 0;
    g_sum = 0;
    int32_t i = 0;
    while (i < ns) {
        int32_t a = small[i];
        int32_t idx = bisect_right_ptr_i32_i32_i32(large, nl, FLOW_CHECKED_DIV((bound), (a)));
        if (idx != nl) {
            g_cnt = (g_cnt + ((int64_t)((nl - idx))));
            g_sum = (g_sum + (((int64_t)(a)) * (ltotal - lpre[idx])));
        }
        i = (i + 1);
    }
}

int64_t compute_T_i64_i32_DivData_DivData(int64_t n, int32_t two, DivData dA, DivData dB) {
    int32_t* small = (int32_t*)(NULL);
    int32_t* large = (int32_t*)(NULL);
    int32_t ns = 0;
    int32_t nl = 0;
    int64_t* preL = (int64_t*)(NULL);
    int64_t sumL = 0;
    if (dA.count <= dB.count) {
        small = dA.divs;
        ns = dA.count;
        large = dB.divs;
        nl = dB.count;
        preL = dB.pre;
        sumL = dB.total;
    } else {
        small = dB.divs;
        ns = dB.count;
        large = dA.divs;
        nl = dA.count;
        preL = dA.pre;
        sumL = dA.total;
    }
    int32_t n_i32 = ((int32_t)(n));
    int32_t bound1 = n_i32;
    int32_t bound2 = FLOW_CHECKED_DIV((n_i32), (two));
    count_sum_products_gt_ptr_i32_i32_ptr_i32_i32_ptr_i64_i64_i32(small, ns, large, nl, preL, sumL, bound1);
    int64_t cnt1 = g_cnt;
    int64_t sum1 = g_sum;
    count_sum_products_gt_ptr_i32_i32_ptr_i32_i32_ptr_i64_i64_i32(small, ns, large, nl, preL, sumL, bound2);
    int64_t cnt2 = g_cnt;
    int64_t sum2 = g_sum;
    int64_t count_total = (cnt1 + cnt2);
    int64_t sum_d = (sum1 + (((int64_t)(two)) * sum2));
    return (sum_d - (n * count_total));
}

int32_t main(void) {
    int32_t N = N_LIMIT;
    build_spf_i32(N);
    int64_t total = 0;
    int32_t lastA = (-1);
    int32_t lastB = (-1);
    DivData dataA = (DivData){ .divs = NULL, .pre = NULL, .count = 0, .total = 0 };
    DivData dataB = (DivData){ .divs = NULL, .pre = NULL, .count = 0, .total = 0 };
    int32_t n = 3;
    while (n <= N) {
        int32_t even;
        int32_t B;
        if ((n & 1) != 0) {
            even = (n - 1);
            B = n;
        } else {
            even = n;
            B = (n - 1);
        }
        int32_t two = (even & (0 - even));
        int32_t A = FLOW_CHECKED_DIV((even), (two));
        if (A != lastA) {
            if (lastA != (-1)) {
                free(dataA.divs);
                free(dataA.pre);
            }
            dataA = divisors_with_prefix_i32(A);
            lastA = A;
        }
        if (B != lastB) {
            if (lastB != (-1)) {
                free(dataB.divs);
                free(dataB.pre);
            }
            dataB = divisors_with_prefix_i32(B);
            lastB = B;
        }
        total = (total + compute_T_i64_i32_DivData_DivData(((int64_t)(n)), two, dataA, dataB));
        n = (n + 1);
    }
    free(dataA.divs);
    free(dataA.pre);
    free(dataB.divs);
    free(dataB.pre);
    free(g_spf);
    printf("%lld\n", total);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%lld\n\00") {addr_space = 0 : i32} : !llvm.array<6 x i8>
  func.func private @calloc(i64, i64) -> !llvm.ptr
  func.func private @free(!llvm.ptr) -> ()
  func.func private @malloc(i64) -> !llvm.ptr
  // Constant: N_LIMIT
  llvm.mlir.global internal constant @N_LIMIT(1234567 : i32) : i32
  // Module static: g_spf
  llvm.mlir.global internal @g_spf() {addr_space = 0 : i32} : !llvm.ptr {
    %0 = llvm.mlir.zero : !llvm.ptr
    llvm.return %0 : !llvm.ptr
  }
  // Module static: g_cnt
  llvm.mlir.global internal @g_cnt(0 : i64) : i64
  // Module static: g_sum
  llvm.mlir.global internal @g_sum(0 : i64) : i64
  func.func @build_spf(%arg0: i32) -> () {
    %2 = arith.extsi %arg0 : i32 to i64
    %3 = arith.constant 1 : i32
    %5 = arith.extsi %3 : i32 to i64
    %4 = arith.addi %2, %5 : i64
    %6 = arith.constant 4 : i32
    %7 = arith.extsi %6 : i32 to i64
    %1 = func.call @calloc(%4, %7) : (i64, i64) -> !llvm.ptr
    %8 = llvm.mlir.addressof @g_spf : !llvm.ptr
    llvm.store %1, %8 : !llvm.ptr, !llvm.ptr
    %10 = arith.extsi %arg0 : i32 to i64
    %11 = arith.constant 1 : i32
    %13 = arith.extsi %11 : i32 to i64
    %12 = arith.addi %10, %13 : i64
    %14 = arith.constant 4 : i32
    %16 = arith.extsi %14 : i32 to i64
    %15 = arith.muli %12, %16 : i64
    %9 = func.call @malloc(%15) : (i64) -> !llvm.ptr
    %17 = arith.constant 0 : i32
    %18 = llvm.mlir.constant(1 : i64) : i64
    %19 = llvm.alloca %18 x i32 : (i64) -> !llvm.ptr
    llvm.store %17, %19 : i32, !llvm.ptr
    %20 = arith.constant 2 : i32
    %21 = llvm.mlir.constant(1 : i64) : i64
    %22 = llvm.alloca %21 x i32 : (i64) -> !llvm.ptr
    llvm.store %20, %22 : i32, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %23 = llvm.load %22 : !llvm.ptr -> i32
    %24 = arith.cmpi sle, %23, %arg0 : i32
    cf.cond_br %24, ^bb1, ^bb2
    ^bb1:
      %26 = llvm.mlir.addressof @g_spf : !llvm.ptr
      %27 = llvm.load %26 : !llvm.ptr -> !llvm.ptr
      %28 = llvm.load %22 : !llvm.ptr -> i32
      %29 = arith.extsi %28 : i32 to i64
      %30 = llvm.getelementptr %27[%29] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %25 = llvm.load %30 : !llvm.ptr -> i32
      %31 = arith.constant 0 : i32
      %32 = arith.cmpi eq, %25, %31 : i32
      cf.cond_br %32, ^bb3, ^bb4
      ^bb3:
        %33 = llvm.load %22 : !llvm.ptr -> i32
        %34 = llvm.mlir.addressof @g_spf : !llvm.ptr
        %35 = llvm.load %34 : !llvm.ptr -> !llvm.ptr
        %36 = llvm.load %22 : !llvm.ptr -> i32
        %37 = arith.extsi %36 : i32 to i64
        %38 = llvm.getelementptr %35[%37] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        llvm.store %33, %38 : i32, !llvm.ptr
        %39 = llvm.load %22 : !llvm.ptr -> i32
        %40 = llvm.load %19 : !llvm.ptr -> i32
        %41 = arith.extsi %40 : i32 to i64
        %42 = llvm.getelementptr %9[%41] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        llvm.store %39, %42 : i32, !llvm.ptr
        %43 = llvm.load %19 : !llvm.ptr -> i32
        %44 = arith.constant 1 : i32
        %45 = arith.addi %43, %44 : i32
        llvm.store %45, %19 : i32, !llvm.ptr
        cf.br ^bb5
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %46 = arith.constant 0 : i32
      %47 = llvm.mlir.constant(1 : i64) : i64
      %48 = llvm.alloca %47 x i32 : (i64) -> !llvm.ptr
      llvm.store %46, %48 : i32, !llvm.ptr
      cf.br ^bb6
      ^bb6:
      %49 = llvm.load %48 : !llvm.ptr -> i32
      %50 = llvm.load %19 : !llvm.ptr -> i32
      %51 = arith.cmpi slt, %49, %50 : i32
      cf.cond_br %51, ^bb7, ^bb8
      ^bb7:
        %52 = llvm.load %22 : !llvm.ptr -> i32
        %54 = llvm.load %48 : !llvm.ptr -> i32
        %55 = arith.extsi %54 : i32 to i64
        %56 = llvm.getelementptr %9[%55] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %53 = llvm.load %56 : !llvm.ptr -> i32
        %57 = arith.muli %52, %53 : i32
        %58 = arith.cmpi sgt, %57, %arg0 : i32
        cf.cond_br %58, ^bb9, ^bb10
        ^bb9:
          cf.br ^bb8
        ^bb10:
          cf.br ^bb11
        ^bb11:
        %60 = llvm.load %48 : !llvm.ptr -> i32
        %61 = arith.extsi %60 : i32 to i64
        %62 = llvm.getelementptr %9[%61] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %59 = llvm.load %62 : !llvm.ptr -> i32
        %63 = llvm.mlir.addressof @g_spf : !llvm.ptr
        %64 = llvm.load %63 : !llvm.ptr -> !llvm.ptr
        %65 = arith.extsi %57 : i32 to i64
        %66 = llvm.getelementptr %64[%65] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        llvm.store %59, %66 : i32, !llvm.ptr
        %68 = llvm.load %48 : !llvm.ptr -> i32
        %69 = arith.extsi %68 : i32 to i64
        %70 = llvm.getelementptr %9[%69] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %67 = llvm.load %70 : !llvm.ptr -> i32
        %72 = llvm.mlir.addressof @g_spf : !llvm.ptr
        %73 = llvm.load %72 : !llvm.ptr -> !llvm.ptr
        %74 = llvm.load %22 : !llvm.ptr -> i32
        %75 = arith.extsi %74 : i32 to i64
        %76 = llvm.getelementptr %73[%75] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %71 = llvm.load %76 : !llvm.ptr -> i32
        %77 = arith.cmpi eq, %67, %71 : i32
        cf.cond_br %77, ^bb12, ^bb13
        ^bb12:
          cf.br ^bb8
        ^bb13:
          cf.br ^bb14
        ^bb14:
        %78 = llvm.load %48 : !llvm.ptr -> i32
        %79 = arith.constant 1 : i32
        %80 = arith.addi %78, %79 : i32
        llvm.store %80, %48 : i32, !llvm.ptr
        cf.br ^bb6
      ^bb8:
      %81 = llvm.load %22 : !llvm.ptr -> i32
      %82 = arith.constant 1 : i32
      %83 = arith.addi %81, %82 : i32
      llvm.store %83, %22 : i32, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    func.call @free(%9) : (!llvm.ptr) -> ()
    %85 = arith.constant 0 : i32
    %86 = llvm.mlir.addressof @g_spf : !llvm.ptr
    %87 = llvm.load %86 : !llvm.ptr -> !llvm.ptr
    %88 = arith.constant 0 : i32
    %89 = arith.extsi %88 : i32 to i64
    %90 = llvm.getelementptr %87[%89] : (!llvm.ptr, i64) -> !llvm.ptr, i32
    llvm.store %85, %90 : i32, !llvm.ptr
    %91 = arith.constant 1 : i32
    %92 = arith.cmpi sge, %arg0, %91 : i32
    cf.cond_br %92, ^bb15, ^bb16
    ^bb15:
      %93 = arith.constant 1 : i32
      %94 = llvm.mlir.addressof @g_spf : !llvm.ptr
      %95 = llvm.load %94 : !llvm.ptr -> !llvm.ptr
      %96 = arith.constant 1 : i32
      %97 = arith.extsi %96 : i32 to i64
      %98 = llvm.getelementptr %95[%97] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %93, %98 : i32, !llvm.ptr
      cf.br ^bb17
    ^bb16:
      cf.br ^bb17
    ^bb17:
    func.return
  }
  // Struct: DivData
  // Fields:
  //   divs: !llvm.ptr
  //   pre: !llvm.ptr
  //   count: i32
  //   total: i64
  func.func @insertion_sort(%arg0: !llvm.ptr, %arg1: i32) -> () {
    %99 = arith.constant 1 : i32
    %100 = llvm.mlir.constant(1 : i64) : i64
    %101 = llvm.alloca %100 x i32 : (i64) -> !llvm.ptr
    llvm.store %99, %101 : i32, !llvm.ptr
    cf.br ^bb18
    ^bb18:
    %102 = llvm.load %101 : !llvm.ptr -> i32
    %103 = arith.cmpi slt, %102, %arg1 : i32
    cf.cond_br %103, ^bb19, ^bb20
    ^bb19:
      %105 = llvm.load %101 : !llvm.ptr -> i32
      %106 = arith.extsi %105 : i32 to i64
      %107 = llvm.getelementptr %arg0[%106] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %104 = llvm.load %107 : !llvm.ptr -> i32
      %108 = llvm.load %101 : !llvm.ptr -> i32
      %109 = arith.constant 1 : i32
      %110 = arith.subi %108, %109 : i32
      %111 = llvm.mlir.constant(1 : i64) : i64
      %112 = llvm.alloca %111 x i32 : (i64) -> !llvm.ptr
      llvm.store %110, %112 : i32, !llvm.ptr
      cf.br ^bb21
      ^bb21:
      %113 = llvm.load %112 : !llvm.ptr -> i32
      %114 = arith.constant 0 : i32
      %115 = arith.cmpi sge, %113, %114 : i32
      cf.cond_br %115, ^bb22, ^bb23
      ^bb22:
        %117 = llvm.load %112 : !llvm.ptr -> i32
        %118 = arith.extsi %117 : i32 to i64
        %119 = llvm.getelementptr %arg0[%118] : (!llvm.ptr, i64) -> !llvm.ptr, i32
        %116 = llvm.load %119 : !llvm.ptr -> i32
        %120 = arith.cmpi sgt, %116, %104 : i32
        cf.cond_br %120, ^bb24, ^bb25
        ^bb24:
          %122 = llvm.load %112 : !llvm.ptr -> i32
          %123 = arith.extsi %122 : i32 to i64
          %124 = llvm.getelementptr %arg0[%123] : (!llvm.ptr, i64) -> !llvm.ptr, i32
          %121 = llvm.load %124 : !llvm.ptr -> i32
          %125 = llvm.load %112 : !llvm.ptr -> i32
          %126 = arith.constant 1 : i32
          %127 = arith.addi %125, %126 : i32
          %128 = arith.extsi %127 : i32 to i64
          %129 = llvm.getelementptr %arg0[%128] : (!llvm.ptr, i64) -> !llvm.ptr, i32
          llvm.store %121, %129 : i32, !llvm.ptr
          %130 = llvm.load %112 : !llvm.ptr -> i32
          %131 = arith.constant 1 : i32
          %132 = arith.subi %130, %131 : i32
          llvm.store %132, %112 : i32, !llvm.ptr
          cf.br ^bb26
        ^bb25:
          cf.br ^bb23
        ^bb26:
        cf.br ^bb21
      ^bb23:
      %133 = llvm.load %112 : !llvm.ptr -> i32
      %134 = arith.constant 1 : i32
      %135 = arith.addi %133, %134 : i32
      %136 = arith.extsi %135 : i32 to i64
      %137 = llvm.getelementptr %arg0[%136] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %104, %137 : i32, !llvm.ptr
      %138 = llvm.load %101 : !llvm.ptr -> i32
      %139 = arith.constant 1 : i32
      %140 = arith.addi %138, %139 : i32
      llvm.store %140, %101 : i32, !llvm.ptr
      cf.br ^bb18
    ^bb20:
    func.return
  }
  func.func @divisors_with_prefix(%arg0: i32) -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)> {
    %141 = arith.constant 1 : i32
    %142 = arith.cmpi eq, %arg0, %141 : i32
    cf.cond_br %142, ^bb27, ^bb28
    ^bb27:
      %144 = arith.constant 4 : i32
      %145 = arith.extsi %144 : i32 to i64
      %143 = func.call @malloc(%145) : (i64) -> !llvm.ptr
      %146 = arith.constant 1 : i32
      %147 = arith.constant 0 : i32
      %148 = arith.extsi %147 : i32 to i64
      %149 = llvm.getelementptr %143[%148] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %146, %149 : i32, !llvm.ptr
      %151 = arith.constant 16 : i32
      %152 = arith.extsi %151 : i32 to i64
      %150 = func.call @malloc(%152) : (i64) -> !llvm.ptr
      %153 = arith.constant 0 : i32
      %154 = arith.constant 0 : i32
      %155 = arith.extsi %153 : i32 to i64
      %156 = arith.extsi %154 : i32 to i64
      %157 = llvm.getelementptr %150[%156] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %155, %157 : i64, !llvm.ptr
      %158 = arith.constant 1 : i32
      %159 = arith.constant 1 : i32
      %160 = arith.extsi %158 : i32 to i64
      %161 = arith.extsi %159 : i32 to i64
      %162 = llvm.getelementptr %150[%161] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %160, %162 : i64, !llvm.ptr
      %163 = llvm.mlir.undef : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %164 = llvm.insertvalue %143, %163[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %165 = llvm.insertvalue %150, %164[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %166 = arith.constant 1 : i32
      %167 = llvm.insertvalue %166, %165[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %168 = arith.constant 1 : i32
      %169 = arith.extsi %168 : i32 to i64
      %170 = llvm.insertvalue %169, %167[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %171 = llvm.mlir.undef : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %172 = llvm.extractvalue %170[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %173 = llvm.insertvalue %172, %171[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %174 = llvm.extractvalue %170[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %175 = llvm.insertvalue %174, %173[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %176 = llvm.extractvalue %170[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %177 = llvm.insertvalue %176, %175[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %178 = llvm.extractvalue %170[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %179 = llvm.insertvalue %178, %177[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %180 = llvm.mlir.constant(1 : i64) : i64
      %181 = llvm.alloca %180 x !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)> : (i64) -> !llvm.ptr
      llvm.store %179, %181 : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>, !llvm.ptr
      %182 = llvm.load %181 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      func.return %182 : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    ^bb28:
      cf.br ^bb29
    ^bb29:
    %184 = arith.constant 256 : i32
    %185 = arith.extsi %184 : i32 to i64
    %183 = func.call @malloc(%185) : (i64) -> !llvm.ptr
    %187 = arith.constant 256 : i32
    %188 = arith.extsi %187 : i32 to i64
    %186 = func.call @malloc(%188) : (i64) -> !llvm.ptr
    %189 = arith.constant 0 : i32
    %190 = llvm.mlir.constant(1 : i64) : i64
    %191 = llvm.alloca %190 x i32 : (i64) -> !llvm.ptr
    llvm.store %189, %191 : i32, !llvm.ptr
    %192 = llvm.mlir.constant(1 : i64) : i64
    %193 = llvm.alloca %192 x i32 : (i64) -> !llvm.ptr
    llvm.store %arg0, %193 : i32, !llvm.ptr
    cf.br ^bb30
    ^bb30:
    %194 = llvm.load %193 : !llvm.ptr -> i32
    %195 = arith.constant 1 : i32
    %196 = arith.cmpi sgt, %194, %195 : i32
    cf.cond_br %196, ^bb31, ^bb32
    ^bb31:
      %198 = llvm.mlir.addressof @g_spf : !llvm.ptr
      %199 = llvm.load %198 : !llvm.ptr -> !llvm.ptr
      %200 = llvm.load %193 : !llvm.ptr -> i32
      %201 = arith.extsi %200 : i32 to i64
      %202 = llvm.getelementptr %199[%201] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %197 = llvm.load %202 : !llvm.ptr -> i32
      %203 = arith.constant 0 : i32
      %204 = llvm.mlir.constant(1 : i64) : i64
      %205 = llvm.alloca %204 x i32 : (i64) -> !llvm.ptr
      llvm.store %203, %205 : i32, !llvm.ptr
      cf.br ^bb33
      ^bb33:
      %206 = llvm.load %193 : !llvm.ptr -> i32
      %207 = arith.remsi %206, %197 : i32
      %208 = arith.constant 0 : i32
      %209 = arith.cmpi eq, %207, %208 : i32
      cf.cond_br %209, ^bb34, ^bb35
      ^bb34:
        %210 = llvm.load %193 : !llvm.ptr -> i32
        %211 = arith.divsi %210, %197 : i32
        llvm.store %211, %193 : i32, !llvm.ptr
        %212 = llvm.load %205 : !llvm.ptr -> i32
        %213 = arith.constant 1 : i32
        %214 = arith.addi %212, %213 : i32
        llvm.store %214, %205 : i32, !llvm.ptr
        cf.br ^bb33
      ^bb35:
      %215 = llvm.load %191 : !llvm.ptr -> i32
      %216 = arith.extsi %215 : i32 to i64
      %217 = llvm.getelementptr %183[%216] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %197, %217 : i32, !llvm.ptr
      %218 = llvm.load %205 : !llvm.ptr -> i32
      %219 = llvm.load %191 : !llvm.ptr -> i32
      %220 = arith.extsi %219 : i32 to i64
      %221 = llvm.getelementptr %186[%220] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      llvm.store %218, %221 : i32, !llvm.ptr
      %222 = llvm.load %191 : !llvm.ptr -> i32
      %223 = arith.constant 1 : i32
      %224 = arith.addi %222, %223 : i32
      llvm.store %224, %191 : i32, !llvm.ptr
      cf.br ^bb30
    ^bb32:
    %225 = arith.constant 1 : i32
    %226 = llvm.mlir.constant(1 : i64) : i64
    %227 = llvm.alloca %226 x i32 : (i64) -> !llvm.ptr
    llvm.store %225, %227 : i32, !llvm.ptr
    %228 = arith.constant 0 : i32
    %229 = llvm.mlir.constant(1 : i64) : i64
    %230 = llvm.alloca %229 x i32 : (i64) -> !llvm.ptr
    llvm.store %228, %230 : i32, !llvm.ptr
    cf.br ^bb36
    ^bb36:
    %231 = llvm.load %230 : !llvm.ptr -> i32
    %232 = llvm.load %191 : !llvm.ptr -> i32
    %233 = arith.cmpi slt, %231, %232 : i32
    cf.cond_br %233, ^bb37, ^bb38
    ^bb37:
      %234 = llvm.load %227 : !llvm.ptr -> i32
      %236 = llvm.load %230 : !llvm.ptr -> i32
      %237 = arith.extsi %236 : i32 to i64
      %238 = llvm.getelementptr %186[%237] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %235 = llvm.load %238 : !llvm.ptr -> i32
      %239 = arith.constant 1 : i32
      %240 = arith.addi %235, %239 : i32
      %241 = arith.muli %234, %240 : i32
      llvm.store %241, %227 : i32, !llvm.ptr
      %242 = llvm.load %230 : !llvm.ptr -> i32
      %243 = arith.constant 1 : i32
      %244 = arith.addi %242, %243 : i32
      llvm.store %244, %230 : i32, !llvm.ptr
      cf.br ^bb36
    ^bb38:
    %246 = llvm.load %227 : !llvm.ptr -> i32
    %247 = arith.extsi %246 : i32 to i64
    %248 = arith.constant 4 : i32
    %250 = arith.extsi %248 : i32 to i64
    %249 = arith.muli %247, %250 : i64
    %245 = func.call @malloc(%249) : (i64) -> !llvm.ptr
    %251 = arith.constant 1 : i32
    %252 = llvm.mlir.constant(1 : i64) : i64
    %253 = llvm.alloca %252 x i32 : (i64) -> !llvm.ptr
    llvm.store %251, %253 : i32, !llvm.ptr
    %254 = arith.constant 1 : i32
    %255 = arith.constant 0 : i32
    %256 = arith.extsi %255 : i32 to i64
    %257 = llvm.getelementptr %245[%256] : (!llvm.ptr, i64) -> !llvm.ptr, i32
    llvm.store %254, %257 : i32, !llvm.ptr
    %258 = arith.constant 0 : i32
    %259 = llvm.mlir.constant(1 : i64) : i64
    %260 = llvm.alloca %259 x i32 : (i64) -> !llvm.ptr
    llvm.store %258, %260 : i32, !llvm.ptr
    cf.br ^bb39
    ^bb39:
    %261 = llvm.load %260 : !llvm.ptr -> i32
    %262 = llvm.load %191 : !llvm.ptr -> i32
    %263 = arith.cmpi slt, %261, %262 : i32
    cf.cond_br %263, ^bb40, ^bb41
    ^bb40:
      %265 = llvm.load %260 : !llvm.ptr -> i32
      %266 = arith.extsi %265 : i32 to i64
      %267 = llvm.getelementptr %183[%266] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %264 = llvm.load %267 : !llvm.ptr -> i32
      %269 = llvm.load %260 : !llvm.ptr -> i32
      %270 = arith.extsi %269 : i32 to i64
      %271 = llvm.getelementptr %186[%270] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %268 = llvm.load %271 : !llvm.ptr -> i32
      %272 = llvm.load %253 : !llvm.ptr -> i32
      %273 = arith.constant 1 : i32
      %274 = llvm.mlir.constant(1 : i64) : i64
      %275 = llvm.alloca %274 x i32 : (i64) -> !llvm.ptr
      llvm.store %273, %275 : i32, !llvm.ptr
      %276 = arith.constant 1 : i32
      %277 = llvm.mlir.constant(1 : i64) : i64
      %278 = llvm.alloca %277 x i32 : (i64) -> !llvm.ptr
      llvm.store %276, %278 : i32, !llvm.ptr
      cf.br ^bb42
      ^bb42:
      %279 = llvm.load %278 : !llvm.ptr -> i32
      %280 = arith.cmpi sle, %279, %268 : i32
      cf.cond_br %280, ^bb43, ^bb44
      ^bb43:
        %281 = llvm.load %275 : !llvm.ptr -> i32
        %282 = arith.muli %281, %264 : i32
        llvm.store %282, %275 : i32, !llvm.ptr
        %283 = arith.constant 0 : i32
        %284 = llvm.mlir.constant(1 : i64) : i64
        %285 = llvm.alloca %284 x i32 : (i64) -> !llvm.ptr
        llvm.store %283, %285 : i32, !llvm.ptr
        cf.br ^bb45
        ^bb45:
        %286 = llvm.load %285 : !llvm.ptr -> i32
        %287 = arith.cmpi slt, %286, %272 : i32
        cf.cond_br %287, ^bb46, ^bb47
        ^bb46:
          %289 = llvm.load %285 : !llvm.ptr -> i32
          %290 = arith.extsi %289 : i32 to i64
          %291 = llvm.getelementptr %245[%290] : (!llvm.ptr, i64) -> !llvm.ptr, i32
          %288 = llvm.load %291 : !llvm.ptr -> i32
          %292 = llvm.load %275 : !llvm.ptr -> i32
          %293 = arith.muli %288, %292 : i32
          %294 = llvm.load %253 : !llvm.ptr -> i32
          %295 = arith.extsi %294 : i32 to i64
          %296 = llvm.getelementptr %245[%295] : (!llvm.ptr, i64) -> !llvm.ptr, i32
          llvm.store %293, %296 : i32, !llvm.ptr
          %297 = llvm.load %253 : !llvm.ptr -> i32
          %298 = arith.constant 1 : i32
          %299 = arith.addi %297, %298 : i32
          llvm.store %299, %253 : i32, !llvm.ptr
          %300 = llvm.load %285 : !llvm.ptr -> i32
          %301 = arith.constant 1 : i32
          %302 = arith.addi %300, %301 : i32
          llvm.store %302, %285 : i32, !llvm.ptr
          cf.br ^bb45
        ^bb47:
        %303 = llvm.load %278 : !llvm.ptr -> i32
        %304 = arith.constant 1 : i32
        %305 = arith.addi %303, %304 : i32
        llvm.store %305, %278 : i32, !llvm.ptr
        cf.br ^bb42
      ^bb44:
      %306 = llvm.load %260 : !llvm.ptr -> i32
      %307 = arith.constant 1 : i32
      %308 = arith.addi %306, %307 : i32
      llvm.store %308, %260 : i32, !llvm.ptr
      cf.br ^bb39
    ^bb41:
    %310 = llvm.load %253 : !llvm.ptr -> i32
    func.call @insertion_sort(%245, %310) : (!llvm.ptr, i32) -> ()
    %312 = llvm.load %253 : !llvm.ptr -> i32
    %313 = arith.extsi %312 : i32 to i64
    %314 = arith.constant 1 : i32
    %316 = arith.extsi %314 : i32 to i64
    %315 = arith.addi %313, %316 : i64
    %317 = arith.constant 8 : i32
    %319 = arith.extsi %317 : i32 to i64
    %318 = arith.muli %315, %319 : i64
    %311 = func.call @malloc(%318) : (i64) -> !llvm.ptr
    %320 = arith.constant 0 : i32
    %321 = arith.extsi %320 : i32 to i64
    %322 = llvm.mlir.constant(1 : i64) : i64
    %323 = llvm.alloca %322 x i64 : (i64) -> !llvm.ptr
    llvm.store %321, %323 : i64, !llvm.ptr
    %324 = arith.constant 0 : i32
    %325 = llvm.mlir.constant(1 : i64) : i64
    %326 = llvm.alloca %325 x i32 : (i64) -> !llvm.ptr
    llvm.store %324, %326 : i32, !llvm.ptr
    cf.br ^bb48
    ^bb48:
    %327 = llvm.load %326 : !llvm.ptr -> i32
    %328 = llvm.load %253 : !llvm.ptr -> i32
    %329 = arith.cmpi slt, %327, %328 : i32
    cf.cond_br %329, ^bb49, ^bb50
    ^bb49:
      %330 = llvm.load %323 : !llvm.ptr -> i64
      %332 = llvm.load %326 : !llvm.ptr -> i32
      %333 = arith.extsi %332 : i32 to i64
      %334 = llvm.getelementptr %245[%333] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %331 = llvm.load %334 : !llvm.ptr -> i32
      %335 = arith.extsi %331 : i32 to i64
      %336 = arith.addi %330, %335 : i64
      llvm.store %336, %323 : i64, !llvm.ptr
      %337 = llvm.load %323 : !llvm.ptr -> i64
      %338 = llvm.load %326 : !llvm.ptr -> i32
      %339 = arith.constant 1 : i32
      %340 = arith.addi %338, %339 : i32
      %341 = arith.extsi %340 : i32 to i64
      %342 = llvm.getelementptr %311[%341] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %337, %342 : i64, !llvm.ptr
      %343 = llvm.load %326 : !llvm.ptr -> i32
      %344 = arith.constant 1 : i32
      %345 = arith.addi %343, %344 : i32
      llvm.store %345, %326 : i32, !llvm.ptr
      cf.br ^bb48
    ^bb50:
    func.call @free(%183) : (!llvm.ptr) -> ()
    func.call @free(%186) : (!llvm.ptr) -> ()
    %348 = llvm.mlir.undef : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %349 = llvm.insertvalue %245, %348[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %350 = llvm.insertvalue %311, %349[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %351 = llvm.load %253 : !llvm.ptr -> i32
    %352 = llvm.insertvalue %351, %350[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %353 = llvm.load %323 : !llvm.ptr -> i64
    %354 = llvm.insertvalue %353, %352[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %355 = llvm.mlir.undef : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %356 = llvm.extractvalue %354[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %357 = llvm.insertvalue %356, %355[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %358 = llvm.extractvalue %354[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %359 = llvm.insertvalue %358, %357[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %360 = llvm.extractvalue %354[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %361 = llvm.insertvalue %360, %359[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %362 = llvm.extractvalue %354[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %363 = llvm.insertvalue %362, %361[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %364 = llvm.mlir.constant(1 : i64) : i64
    %365 = llvm.alloca %364 x !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)> : (i64) -> !llvm.ptr
    llvm.store %363, %365 : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>, !llvm.ptr
    %366 = llvm.load %365 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    func.return %366 : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
  }
  func.func @bisect_right(%arg0: !llvm.ptr, %arg1: i32, %arg2: i32) -> i32 {
    %367 = arith.constant 0 : i32
    %368 = llvm.mlir.constant(1 : i64) : i64
    %369 = llvm.alloca %368 x i32 : (i64) -> !llvm.ptr
    llvm.store %367, %369 : i32, !llvm.ptr
    %370 = llvm.mlir.constant(1 : i64) : i64
    %371 = llvm.alloca %370 x i32 : (i64) -> !llvm.ptr
    llvm.store %arg1, %371 : i32, !llvm.ptr
    cf.br ^bb51
    ^bb51:
    %372 = llvm.load %369 : !llvm.ptr -> i32
    %373 = llvm.load %371 : !llvm.ptr -> i32
    %374 = arith.cmpi slt, %372, %373 : i32
    cf.cond_br %374, ^bb52, ^bb53
    ^bb52:
      %375 = llvm.load %369 : !llvm.ptr -> i32
      %376 = llvm.load %371 : !llvm.ptr -> i32
      %377 = arith.addi %375, %376 : i32
      %378 = arith.constant 2 : i32
      %379 = arith.divsi %377, %378 : i32
      %381 = arith.extsi %379 : i32 to i64
      %382 = llvm.getelementptr %arg0[%381] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %380 = llvm.load %382 : !llvm.ptr -> i32
      %383 = arith.cmpi sle, %380, %arg2 : i32
      cf.cond_br %383, ^bb54, ^bb55
      ^bb54:
        %384 = arith.constant 1 : i32
        %385 = arith.addi %379, %384 : i32
        llvm.store %385, %369 : i32, !llvm.ptr
        cf.br ^bb56
      ^bb55:
        llvm.store %379, %371 : i32, !llvm.ptr
        cf.br ^bb56
      ^bb56:
      cf.br ^bb51
    ^bb53:
    %386 = llvm.load %369 : !llvm.ptr -> i32
    func.return %386 : i32
  }
  func.func @count_sum_products_gt(%arg0: !llvm.ptr, %arg1: i32, %arg2: !llvm.ptr, %arg3: i32, %arg4: !llvm.ptr, %arg5: i64, %arg6: i32) -> () {
    %387 = arith.constant 0 : i32
    %388 = arith.extsi %387 : i32 to i64
    %389 = llvm.mlir.addressof @g_cnt : !llvm.ptr
    llvm.store %388, %389 : i64, !llvm.ptr
    %390 = arith.constant 0 : i32
    %391 = arith.extsi %390 : i32 to i64
    %392 = llvm.mlir.addressof @g_sum : !llvm.ptr
    llvm.store %391, %392 : i64, !llvm.ptr
    %393 = arith.constant 0 : i32
    %394 = llvm.mlir.constant(1 : i64) : i64
    %395 = llvm.alloca %394 x i32 : (i64) -> !llvm.ptr
    llvm.store %393, %395 : i32, !llvm.ptr
    cf.br ^bb57
    ^bb57:
    %396 = llvm.load %395 : !llvm.ptr -> i32
    %397 = arith.cmpi slt, %396, %arg1 : i32
    cf.cond_br %397, ^bb58, ^bb59
    ^bb58:
      %399 = llvm.load %395 : !llvm.ptr -> i32
      %400 = arith.extsi %399 : i32 to i64
      %401 = llvm.getelementptr %arg0[%400] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %398 = llvm.load %401 : !llvm.ptr -> i32
      %403 = arith.divsi %arg6, %398 : i32
      %402 = func.call @bisect_right(%arg2, %arg3, %403) : (!llvm.ptr, i32, i32) -> i32
      %404 = arith.cmpi ne, %402, %arg3 : i32
      cf.cond_br %404, ^bb60, ^bb61
      ^bb60:
        %405 = llvm.mlir.addressof @g_cnt : !llvm.ptr
        %406 = llvm.load %405 : !llvm.ptr -> i64
        %407 = arith.subi %arg3, %402 : i32
        %408 = arith.extsi %407 : i32 to i64
        %409 = arith.addi %406, %408 : i64
        %410 = llvm.mlir.addressof @g_cnt : !llvm.ptr
        llvm.store %409, %410 : i64, !llvm.ptr
        %411 = llvm.mlir.addressof @g_sum : !llvm.ptr
        %412 = llvm.load %411 : !llvm.ptr -> i64
        %413 = arith.extsi %398 : i32 to i64
        %415 = arith.extsi %402 : i32 to i64
        %416 = llvm.getelementptr %arg4[%415] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %414 = llvm.load %416 : !llvm.ptr -> i64
        %417 = arith.subi %arg5, %414 : i64
        %418 = arith.muli %413, %417 : i64
        %419 = arith.addi %412, %418 : i64
        %420 = llvm.mlir.addressof @g_sum : !llvm.ptr
        llvm.store %419, %420 : i64, !llvm.ptr
        cf.br ^bb62
      ^bb61:
        cf.br ^bb62
      ^bb62:
      %421 = llvm.load %395 : !llvm.ptr -> i32
      %422 = arith.constant 1 : i32
      %423 = arith.addi %421, %422 : i32
      llvm.store %423, %395 : i32, !llvm.ptr
      cf.br ^bb57
    ^bb59:
    func.return
  }
  func.func @compute_T(%arg0: i64, %arg1: i32, %arg2: !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>, %arg3: !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>) -> i64 {
    %424 = llvm.mlir.undef : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %425 = llvm.extractvalue %arg2[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %426 = llvm.insertvalue %425, %424[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %427 = llvm.extractvalue %arg2[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %428 = llvm.insertvalue %427, %426[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %429 = llvm.extractvalue %arg2[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %430 = llvm.insertvalue %429, %428[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %431 = llvm.extractvalue %arg2[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %432 = llvm.insertvalue %431, %430[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %433 = llvm.mlir.constant(1 : i64) : i64
    %434 = llvm.alloca %433 x !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)> : (i64) -> !llvm.ptr
    llvm.store %432, %434 : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>, !llvm.ptr
    %435 = llvm.mlir.undef : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %436 = llvm.extractvalue %arg3[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %437 = llvm.insertvalue %436, %435[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %438 = llvm.extractvalue %arg3[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %439 = llvm.insertvalue %438, %437[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %440 = llvm.extractvalue %arg3[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %441 = llvm.insertvalue %440, %439[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %442 = llvm.extractvalue %arg3[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %443 = llvm.insertvalue %442, %441[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %444 = llvm.mlir.constant(1 : i64) : i64
    %445 = llvm.alloca %444 x !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)> : (i64) -> !llvm.ptr
    llvm.store %443, %445 : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>, !llvm.ptr
    %446 = llvm.mlir.zero : !llvm.ptr
    %447 = llvm.mlir.constant(1 : i64) : i64
    %448 = llvm.alloca %447 x !llvm.ptr : (i64) -> !llvm.ptr
    llvm.store %446, %448 : !llvm.ptr, !llvm.ptr
    %449 = llvm.mlir.zero : !llvm.ptr
    %450 = llvm.mlir.constant(1 : i64) : i64
    %451 = llvm.alloca %450 x !llvm.ptr : (i64) -> !llvm.ptr
    llvm.store %449, %451 : !llvm.ptr, !llvm.ptr
    %452 = arith.constant 0 : i32
    %453 = llvm.mlir.constant(1 : i64) : i64
    %454 = llvm.alloca %453 x i32 : (i64) -> !llvm.ptr
    llvm.store %452, %454 : i32, !llvm.ptr
    %455 = arith.constant 0 : i32
    %456 = llvm.mlir.constant(1 : i64) : i64
    %457 = llvm.alloca %456 x i32 : (i64) -> !llvm.ptr
    llvm.store %455, %457 : i32, !llvm.ptr
    %458 = llvm.mlir.zero : !llvm.ptr
    %459 = llvm.mlir.constant(1 : i64) : i64
    %460 = llvm.alloca %459 x !llvm.ptr : (i64) -> !llvm.ptr
    llvm.store %458, %460 : !llvm.ptr, !llvm.ptr
    %461 = arith.constant 0 : i32
    %462 = arith.extsi %461 : i32 to i64
    %463 = llvm.mlir.constant(1 : i64) : i64
    %464 = llvm.alloca %463 x i64 : (i64) -> !llvm.ptr
    llvm.store %462, %464 : i64, !llvm.ptr
    %465 = llvm.load %434 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %466 = llvm.getelementptr %434[0, 2] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %467 = llvm.load %466 : !llvm.ptr -> i32
    %468 = llvm.load %445 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %469 = llvm.getelementptr %445[0, 2] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %470 = llvm.load %469 : !llvm.ptr -> i32
    %471 = arith.cmpi sle, %467, %470 : i32
    cf.cond_br %471, ^bb63, ^bb64
    ^bb63:
      %472 = llvm.load %434 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %473 = llvm.getelementptr %434[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %474 = llvm.load %473 : !llvm.ptr -> !llvm.ptr
      llvm.store %474, %448 : !llvm.ptr, !llvm.ptr
      %475 = llvm.load %434 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %476 = llvm.getelementptr %434[0, 2] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %477 = llvm.load %476 : !llvm.ptr -> i32
      llvm.store %477, %454 : i32, !llvm.ptr
      %478 = llvm.load %445 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %479 = llvm.getelementptr %445[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %480 = llvm.load %479 : !llvm.ptr -> !llvm.ptr
      llvm.store %480, %451 : !llvm.ptr, !llvm.ptr
      %481 = llvm.load %445 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %482 = llvm.getelementptr %445[0, 2] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %483 = llvm.load %482 : !llvm.ptr -> i32
      llvm.store %483, %457 : i32, !llvm.ptr
      %484 = llvm.load %445 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %485 = llvm.getelementptr %445[0, 1] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %486 = llvm.load %485 : !llvm.ptr -> !llvm.ptr
      llvm.store %486, %460 : !llvm.ptr, !llvm.ptr
      %487 = llvm.load %445 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %488 = llvm.getelementptr %445[0, 3] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %489 = llvm.load %488 : !llvm.ptr -> i64
      llvm.store %489, %464 : i64, !llvm.ptr
      cf.br ^bb65
    ^bb64:
      %490 = llvm.load %445 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %491 = llvm.getelementptr %445[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %492 = llvm.load %491 : !llvm.ptr -> !llvm.ptr
      llvm.store %492, %448 : !llvm.ptr, !llvm.ptr
      %493 = llvm.load %445 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %494 = llvm.getelementptr %445[0, 2] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %495 = llvm.load %494 : !llvm.ptr -> i32
      llvm.store %495, %454 : i32, !llvm.ptr
      %496 = llvm.load %434 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %497 = llvm.getelementptr %434[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %498 = llvm.load %497 : !llvm.ptr -> !llvm.ptr
      llvm.store %498, %451 : !llvm.ptr, !llvm.ptr
      %499 = llvm.load %434 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %500 = llvm.getelementptr %434[0, 2] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %501 = llvm.load %500 : !llvm.ptr -> i32
      llvm.store %501, %457 : i32, !llvm.ptr
      %502 = llvm.load %434 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %503 = llvm.getelementptr %434[0, 1] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %504 = llvm.load %503 : !llvm.ptr -> !llvm.ptr
      llvm.store %504, %460 : !llvm.ptr, !llvm.ptr
      %505 = llvm.load %434 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %506 = llvm.getelementptr %434[0, 3] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %507 = llvm.load %506 : !llvm.ptr -> i64
      llvm.store %507, %464 : i64, !llvm.ptr
      cf.br ^bb65
    ^bb65:
    %508 = arith.trunci %arg0 : i64 to i32
    %509 = arith.divsi %508, %arg1 : i32
    %511 = llvm.load %448 : !llvm.ptr -> !llvm.ptr
    %512 = llvm.load %454 : !llvm.ptr -> i32
    %513 = llvm.load %451 : !llvm.ptr -> !llvm.ptr
    %514 = llvm.load %457 : !llvm.ptr -> i32
    %515 = llvm.load %460 : !llvm.ptr -> !llvm.ptr
    %516 = llvm.load %464 : !llvm.ptr -> i64
    func.call @count_sum_products_gt(%511, %512, %513, %514, %515, %516, %508) : (!llvm.ptr, i32, !llvm.ptr, i32, !llvm.ptr, i64, i32) -> ()
    %517 = llvm.mlir.addressof @g_cnt : !llvm.ptr
    %518 = llvm.load %517 : !llvm.ptr -> i64
    %519 = llvm.mlir.addressof @g_sum : !llvm.ptr
    %520 = llvm.load %519 : !llvm.ptr -> i64
    %522 = llvm.load %448 : !llvm.ptr -> !llvm.ptr
    %523 = llvm.load %454 : !llvm.ptr -> i32
    %524 = llvm.load %451 : !llvm.ptr -> !llvm.ptr
    %525 = llvm.load %457 : !llvm.ptr -> i32
    %526 = llvm.load %460 : !llvm.ptr -> !llvm.ptr
    %527 = llvm.load %464 : !llvm.ptr -> i64
    func.call @count_sum_products_gt(%522, %523, %524, %525, %526, %527, %509) : (!llvm.ptr, i32, !llvm.ptr, i32, !llvm.ptr, i64, i32) -> ()
    %528 = llvm.mlir.addressof @g_cnt : !llvm.ptr
    %529 = llvm.load %528 : !llvm.ptr -> i64
    %530 = llvm.mlir.addressof @g_sum : !llvm.ptr
    %531 = llvm.load %530 : !llvm.ptr -> i64
    %532 = arith.addi %518, %529 : i64
    %533 = arith.extsi %arg1 : i32 to i64
    %534 = arith.muli %533, %531 : i64
    %535 = arith.addi %520, %534 : i64
    %536 = arith.muli %arg0, %532 : i64
    %537 = arith.subi %535, %536 : i64
    func.return %537 : i64
  }
  func.func @main() -> i32 {
    %538 = llvm.mlir.addressof @N_LIMIT : !llvm.ptr
    %539 = llvm.load %538 : !llvm.ptr -> i32
    func.call @build_spf(%539) : (i32) -> ()
    %541 = arith.constant 0 : i32
    %542 = arith.extsi %541 : i32 to i64
    %543 = llvm.mlir.constant(1 : i64) : i64
    %544 = llvm.alloca %543 x i64 : (i64) -> !llvm.ptr
    llvm.store %542, %544 : i64, !llvm.ptr
    %545 = arith.constant 1 : i32
    %547 = arith.constant 0 : i32
    %546 = arith.subi %547, %545 : i32
    %548 = llvm.mlir.constant(1 : i64) : i64
    %549 = llvm.alloca %548 x i32 : (i64) -> !llvm.ptr
    llvm.store %546, %549 : i32, !llvm.ptr
    %550 = arith.constant 1 : i32
    %552 = arith.constant 0 : i32
    %551 = arith.subi %552, %550 : i32
    %553 = llvm.mlir.constant(1 : i64) : i64
    %554 = llvm.alloca %553 x i32 : (i64) -> !llvm.ptr
    llvm.store %551, %554 : i32, !llvm.ptr
    %555 = llvm.mlir.undef : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %556 = llvm.mlir.zero : !llvm.ptr
    %557 = llvm.insertvalue %556, %555[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %558 = llvm.mlir.zero : !llvm.ptr
    %559 = llvm.insertvalue %558, %557[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %560 = arith.constant 0 : i32
    %561 = llvm.insertvalue %560, %559[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %562 = arith.constant 0 : i32
    %563 = arith.extsi %562 : i32 to i64
    %564 = llvm.insertvalue %563, %561[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %565 = llvm.mlir.constant(1 : i64) : i64
    %566 = llvm.alloca %565 x !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)> : (i64) -> !llvm.ptr
    llvm.store %564, %566 : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>, !llvm.ptr
    %567 = llvm.mlir.undef : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %568 = llvm.mlir.zero : !llvm.ptr
    %569 = llvm.insertvalue %568, %567[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %570 = llvm.mlir.zero : !llvm.ptr
    %571 = llvm.insertvalue %570, %569[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %572 = arith.constant 0 : i32
    %573 = llvm.insertvalue %572, %571[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %574 = arith.constant 0 : i32
    %575 = arith.extsi %574 : i32 to i64
    %576 = llvm.insertvalue %575, %573[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %577 = llvm.mlir.constant(1 : i64) : i64
    %578 = llvm.alloca %577 x !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)> : (i64) -> !llvm.ptr
    llvm.store %576, %578 : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>, !llvm.ptr
    %579 = arith.constant 3 : i32
    %580 = llvm.mlir.constant(1 : i64) : i64
    %581 = llvm.alloca %580 x i32 : (i64) -> !llvm.ptr
    llvm.store %579, %581 : i32, !llvm.ptr
    cf.br ^bb66
    ^bb66:
    %582 = llvm.load %581 : !llvm.ptr -> i32
    %583 = arith.cmpi sle, %582, %539 : i32
    cf.cond_br %583, ^bb67, ^bb68
    ^bb67:
      %584 = llvm.mlir.undef : i32
      %585 = llvm.mlir.undef : i32
      %586 = llvm.load %581 : !llvm.ptr -> i32
      %587 = arith.constant 1 : i32
      %588 = arith.andi %586, %587 : i32
      %589 = arith.constant 0 : i32
      %590 = arith.cmpi ne, %588, %589 : i32
      %591, %592 = scf.if %590 -> (i32, i32) {
        %593 = llvm.load %581 : !llvm.ptr -> i32
        %594 = arith.constant 1 : i32
        %595 = arith.subi %593, %594 : i32
        %596 = llvm.load %581 : !llvm.ptr -> i32
        scf.yield %595, %596 : i32, i32
      } else {
        %597 = llvm.load %581 : !llvm.ptr -> i32
        %598 = llvm.load %581 : !llvm.ptr -> i32
        %599 = arith.constant 1 : i32
        %600 = arith.subi %598, %599 : i32
        scf.yield %597, %600 : i32, i32
      }
      %601 = arith.constant 0 : i32
      %602 = arith.subi %601, %591 : i32
      %603 = arith.andi %591, %602 : i32
      %604 = arith.divsi %591, %603 : i32
      %605 = llvm.load %549 : !llvm.ptr -> i32
      %606 = arith.cmpi ne, %604, %605 : i32
      cf.cond_br %606, ^bb69, ^bb70
      ^bb69:
        %607 = llvm.load %549 : !llvm.ptr -> i32
        %608 = arith.constant 1 : i32
        %610 = arith.constant 0 : i32
        %609 = arith.subi %610, %608 : i32
        %611 = arith.cmpi ne, %607, %609 : i32
        cf.cond_br %611, ^bb72, ^bb73
        ^bb72:
          %613 = llvm.load %566 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
          %614 = llvm.getelementptr %566[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
          %615 = llvm.load %614 : !llvm.ptr -> !llvm.ptr
          func.call @free(%615) : (!llvm.ptr) -> ()
          %617 = llvm.load %566 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
          %618 = llvm.getelementptr %566[0, 1] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
          %619 = llvm.load %618 : !llvm.ptr -> !llvm.ptr
          func.call @free(%619) : (!llvm.ptr) -> ()
          cf.br ^bb74
        ^bb73:
          cf.br ^bb74
        ^bb74:
        %620 = func.call @divisors_with_prefix(%604) : (i32) -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %621 = llvm.mlir.undef : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %622 = llvm.extractvalue %620[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %623 = llvm.insertvalue %622, %621[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %624 = llvm.extractvalue %620[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %625 = llvm.insertvalue %624, %623[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %626 = llvm.extractvalue %620[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %627 = llvm.insertvalue %626, %625[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %628 = llvm.extractvalue %620[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %629 = llvm.insertvalue %628, %627[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %630 = llvm.mlir.constant(1 : i64) : i64
        %631 = llvm.alloca %630 x !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)> : (i64) -> !llvm.ptr
        llvm.store %629, %631 : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>, !llvm.ptr
        %632 = llvm.load %631 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        llvm.store %632, %566 : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>, !llvm.ptr
        llvm.store %604, %549 : i32, !llvm.ptr
        cf.br ^bb71
      ^bb70:
        cf.br ^bb71
      ^bb71:
      %633 = llvm.load %554 : !llvm.ptr -> i32
      %634 = arith.cmpi ne, %592, %633 : i32
      cf.cond_br %634, ^bb75, ^bb76
      ^bb75:
        %635 = llvm.load %554 : !llvm.ptr -> i32
        %636 = arith.constant 1 : i32
        %638 = arith.constant 0 : i32
        %637 = arith.subi %638, %636 : i32
        %639 = arith.cmpi ne, %635, %637 : i32
        cf.cond_br %639, ^bb78, ^bb79
        ^bb78:
          %641 = llvm.load %578 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
          %642 = llvm.getelementptr %578[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
          %643 = llvm.load %642 : !llvm.ptr -> !llvm.ptr
          func.call @free(%643) : (!llvm.ptr) -> ()
          %645 = llvm.load %578 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
          %646 = llvm.getelementptr %578[0, 1] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
          %647 = llvm.load %646 : !llvm.ptr -> !llvm.ptr
          func.call @free(%647) : (!llvm.ptr) -> ()
          cf.br ^bb80
        ^bb79:
          cf.br ^bb80
        ^bb80:
        %648 = func.call @divisors_with_prefix(%592) : (i32) -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %649 = llvm.mlir.undef : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %650 = llvm.extractvalue %648[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %651 = llvm.insertvalue %650, %649[0] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %652 = llvm.extractvalue %648[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %653 = llvm.insertvalue %652, %651[1] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %654 = llvm.extractvalue %648[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %655 = llvm.insertvalue %654, %653[2] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %656 = llvm.extractvalue %648[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %657 = llvm.insertvalue %656, %655[3] : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        %658 = llvm.mlir.constant(1 : i64) : i64
        %659 = llvm.alloca %658 x !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)> : (i64) -> !llvm.ptr
        llvm.store %657, %659 : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>, !llvm.ptr
        %660 = llvm.load %659 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
        llvm.store %660, %578 : !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>, !llvm.ptr
        llvm.store %592, %554 : i32, !llvm.ptr
        cf.br ^bb77
      ^bb76:
        cf.br ^bb77
      ^bb77:
      %661 = llvm.load %544 : !llvm.ptr -> i64
      %663 = llvm.load %581 : !llvm.ptr -> i32
      %664 = arith.extsi %663 : i32 to i64
      %665 = llvm.load %566 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %666 = llvm.load %578 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
      %662 = func.call @compute_T(%664, %603, %665, %666) : (i64, i32, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>) -> i64
      %667 = arith.addi %661, %662 : i64
      llvm.store %667, %544 : i64, !llvm.ptr
      %668 = llvm.load %581 : !llvm.ptr -> i32
      %669 = arith.constant 1 : i32
      %670 = arith.addi %668, %669 : i32
      llvm.store %670, %581 : i32, !llvm.ptr
      cf.br ^bb66
    ^bb68:
    %672 = llvm.load %566 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %673 = llvm.getelementptr %566[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %674 = llvm.load %673 : !llvm.ptr -> !llvm.ptr
    func.call @free(%674) : (!llvm.ptr) -> ()
    %676 = llvm.load %566 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %677 = llvm.getelementptr %566[0, 1] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %678 = llvm.load %677 : !llvm.ptr -> !llvm.ptr
    func.call @free(%678) : (!llvm.ptr) -> ()
    %680 = llvm.load %578 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %681 = llvm.getelementptr %578[0, 0] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %682 = llvm.load %681 : !llvm.ptr -> !llvm.ptr
    func.call @free(%682) : (!llvm.ptr) -> ()
    %684 = llvm.load %578 : !llvm.ptr -> !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %685 = llvm.getelementptr %578[0, 1] : (!llvm.ptr) -> !llvm.ptr, !llvm.struct<(!llvm.ptr, !llvm.ptr, i32, i64)>
    %686 = llvm.load %685 : !llvm.ptr -> !llvm.ptr
    func.call @free(%686) : (!llvm.ptr) -> ()
    %688 = llvm.mlir.addressof @g_spf : !llvm.ptr
    %689 = llvm.load %688 : !llvm.ptr -> !llvm.ptr
    func.call @free(%689) : (!llvm.ptr) -> ()
    %690 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %691 = llvm.load %544 : !llvm.ptr -> i64
    %692 = llvm.call @printf(%690, %691) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    %693 = arith.constant 0 : i32
    func.return %693 : i32
  }
}