Problem 075

How many values of L ≤ 1,500,000 can form exactly one integer sided right triangle?

Answer161667
Output161667
StatusPASS
Native helperno
Runtime0 ms
Peak memory7008 KB
Time complexityO(n^3) (estimated)
Space complexityO(n) (estimated)

Performance comparison

MetricOur solutionBest known
Time complexityO(n^3)O(n^2)
Space complexityO(n)O(n^2)
ApproachFlow solutionBottom-up DP
VerdictSuboptimal

Flow source

# Project Euler 075
# How many values of L ≤ 1,500,000 can form exactly one integer sided right triangle?

import euler.nt { gcd }

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

function main() -> i32 {
    let limit: i64 = 1500000
    let counts: ptr<i32> = calloc(limit + 1, 4)
    if counts == null { return 1 }

    # generate primitives via m>n>0, m-n odd, gcd=1
    let mut m: i64 = 2
    while 2 * m * (m + 1) <= limit {
        let mut n: i64 = 1 + (m % 2)  # opposite parity
        while n < m {
            if gcd(m, n) == 1 {
                let a: i64 = m * m - n * n
                let b: i64 = 2 * m * n
                let c: i64 = m * m + n * n
                let peri: i64 = a + b + c
                let mut L: i64 = peri
                while L <= limit {
                    counts[L as i32] = counts[L as i32] + 1
                    L = L + peri
                }
            }
            n = n + 2
        }
        m = m + 1
    }

    let mut ans: i64 = 0
    for i in 1..(limit + 1) {
        if counts[i as i32] == 1 { ans = ans + 1 }
    }
    printf("%lld\n", ans)
    free(counts)
    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; }

int64_t gcd_i64_i64(int64_t a0, int64_t b0);
int64_t lcm_i64_i64(int64_t a, int64_t b);
int64_t isqrt_i64(int64_t n);
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod);
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod);
bool is_prime_i64(int64_t n);
int32_t main(void);

int64_t gcd_i64_i64(int64_t a0, int64_t b0) {
    int64_t a = a0;
    int64_t b = b0;
    while (b != 0) {
        int64_t t = FLOW_CHECKED_MOD((a), (b));
        a = b;
        b = t;
    }
    return a;
}

int64_t lcm_i64_i64(int64_t a, int64_t b) {
    if ((a == 0 || b == 0)) {
        return 0;
    }
    return (FLOW_CHECKED_DIV((a), (gcd_i64_i64(a, b))) * b);
}

int64_t isqrt_i64(int64_t n) {
    if (n < 2) {
        return n;
    }
    int64_t x = n;
    int64_t y = FLOW_CHECKED_DIV(((x + 1)), (2));
    while (y < x) {
        x = y;
        y = FLOW_CHECKED_DIV(((x + FLOW_CHECKED_DIV((n), (x)))), (2));
    }
    return x;
}

int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod) {
    int64_t a = FLOW_CHECKED_MOD((a0), (mod));
    int64_t b = FLOW_CHECKED_MOD((b0), (mod));
    int64_t result = 0;
    while (b > 0) {
        if (FLOW_CHECKED_MOD((b), (2)) == 1) {
            result = FLOW_CHECKED_MOD(((result + a)), (mod));
        }
        a = FLOW_CHECKED_MOD(((a * 2)), (mod));
        b = FLOW_CHECKED_DIV((b), (2));
    }
    return result;
}

int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod) {
    if (mod == 1) {
        return 0;
    }
    int64_t result = 1;
    int64_t b = FLOW_CHECKED_MOD((base), (mod));
    int64_t e = exp;
    while (e > 0) {
        if (FLOW_CHECKED_MOD((e), (2)) == 1) {
            result = mulmod_i64_i64_i64(result, b, mod);
        }
        b = mulmod_i64_i64_i64(b, b, mod);
        e = FLOW_CHECKED_DIV((e), (2));
    }
    return result;
}

bool is_prime_i64(int64_t n) {
    if (n < 2) {
        return 0;
    }
    if (n < 4) {
        return 1;
    }
    if ((FLOW_CHECKED_MOD((n), (2)) == 0 || FLOW_CHECKED_MOD((n), (3)) == 0)) {
        return 0;
    }
    int64_t i = 5;
    while ((i * i) <= n) {
        if ((FLOW_CHECKED_MOD((n), (i)) == 0 || FLOW_CHECKED_MOD((n), ((i + 2))) == 0)) {
            return 0;
        }
        i = (i + 6);
    }
    return 1;
}



int32_t main(void) {
    int64_t limit = 1500000;
    int32_t* counts = (int32_t*)(calloc((limit + 1), 4));
    if (counts == NULL) {
        return 1;
    }
    int64_t m = 2;
    while (((2 * m) * (m + 1)) <= limit) {
        int64_t n = (1 + FLOW_CHECKED_MOD((m), (2)));
        while (n < m) {
            if (gcd_i64_i64(m, n) == 1) {
                int64_t a = ((m * m) - (n * n));
                int64_t b = ((2 * m) * n);
                int64_t c = ((m * m) + (n * n));
                int64_t peri = ((a + b) + c);
                int64_t L = peri;
                while (L <= limit) {
                    counts[((int32_t)(L))] = (counts[((int32_t)(L))] + 1);
                    L = (L + peri);
                }
            }
            n = (n + 2);
        }
        m = (m + 1);
    }
    int64_t ans = 0;
    int32_t __flow_step_1 = 1;
    for (int32_t i = 1; (1 <= (limit + 1)) ? i < (limit + 1) : i > (limit + 1); i += (1 <= (limit + 1)) ? 1 : -1) {
        if (counts[((int32_t)(i))] == 1) {
            ans = (ans + 1);
        }
    }
    printf("%lld\n", ans);
    free(counts);
    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 @gcd(%arg0: i64, %arg1: i64) -> i64 {
    %0 = llvm.mlir.constant(1 : i64) : i64
    %1 = llvm.alloca %0 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %1 : i64, !llvm.ptr
    %2 = llvm.mlir.constant(1 : i64) : i64
    %3 = llvm.alloca %2 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg1, %3 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %4 = llvm.load %3 : !llvm.ptr -> i64
    %5 = arith.constant 0 : i32
    %7 = arith.extsi %5 : i32 to i64
    %6 = arith.cmpi ne, %4, %7 : i64
    cf.cond_br %6, ^bb1, ^bb2
    ^bb1:
      %8 = llvm.load %1 : !llvm.ptr -> i64
      %9 = llvm.load %3 : !llvm.ptr -> i64
      %10 = arith.remsi %8, %9 : i64
      %11 = llvm.load %3 : !llvm.ptr -> i64
      llvm.store %11, %1 : i64, !llvm.ptr
      llvm.store %10, %3 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %12 = llvm.load %1 : !llvm.ptr -> i64
    func.return %12 : i64
  }
  func.func @lcm(%arg0: i64, %arg1: i64) -> i64 {
    %13 = arith.constant 0 : i32
    %15 = arith.extsi %13 : i32 to i64
    %14 = arith.cmpi eq, %arg0, %15 : i64
    %16 = scf.if %14 -> (i1) {
      %17 = arith.constant true
      scf.yield %17 : i1
    } else {
      %18 = arith.constant 0 : i32
      %20 = arith.extsi %18 : i32 to i64
      %19 = arith.cmpi eq, %arg1, %20 : i64
      scf.yield %19 : i1
    }
    cf.cond_br %16, ^bb3, ^bb4
    ^bb3:
      %21 = arith.constant 0 : i32
      %22 = arith.extsi %21 : i32 to i64
      func.return %22 : i64
    ^bb4:
      cf.br ^bb5
    ^bb5:
    %23 = func.call @gcd(%arg0, %arg1) : (i64, i64) -> i64
    %24 = arith.divsi %arg0, %23 : i64
    %25 = arith.muli %24, %arg1 : i64
    func.return %25 : i64
  }
  func.func @isqrt(%arg0: i64) -> i64 {
    %26 = arith.constant 2 : i32
    %28 = arith.extsi %26 : i32 to i64
    %27 = arith.cmpi slt, %arg0, %28 : i64
    cf.cond_br %27, ^bb6, ^bb7
    ^bb6:
      func.return %arg0 : i64
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %29 = llvm.mlir.constant(1 : i64) : i64
    %30 = llvm.alloca %29 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %30 : i64, !llvm.ptr
    %31 = llvm.load %30 : !llvm.ptr -> i64
    %32 = arith.constant 1 : i32
    %34 = arith.extsi %32 : i32 to i64
    %33 = arith.addi %31, %34 : i64
    %35 = arith.constant 2 : i32
    %37 = arith.extsi %35 : i32 to i64
    %36 = arith.divsi %33, %37 : i64
    %38 = llvm.mlir.constant(1 : i64) : i64
    %39 = llvm.alloca %38 x i64 : (i64) -> !llvm.ptr
    llvm.store %36, %39 : i64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %40 = llvm.load %39 : !llvm.ptr -> i64
    %41 = llvm.load %30 : !llvm.ptr -> i64
    %42 = arith.cmpi slt, %40, %41 : i64
    cf.cond_br %42, ^bb10, ^bb11
    ^bb10:
      %43 = llvm.load %39 : !llvm.ptr -> i64
      llvm.store %43, %30 : i64, !llvm.ptr
      %44 = llvm.load %30 : !llvm.ptr -> i64
      %45 = llvm.load %30 : !llvm.ptr -> i64
      %46 = arith.divsi %arg0, %45 : i64
      %47 = arith.addi %44, %46 : i64
      %48 = arith.constant 2 : i32
      %50 = arith.extsi %48 : i32 to i64
      %49 = arith.divsi %47, %50 : i64
      llvm.store %49, %39 : i64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %51 = llvm.load %30 : !llvm.ptr -> i64
    func.return %51 : i64
  }
  func.func @mulmod(%arg0: i64, %arg1: i64, %arg2: i64) -> i64 {
    %52 = arith.remsi %arg0, %arg2 : i64
    %53 = llvm.mlir.constant(1 : i64) : i64
    %54 = llvm.alloca %53 x i64 : (i64) -> !llvm.ptr
    llvm.store %52, %54 : i64, !llvm.ptr
    %55 = arith.remsi %arg1, %arg2 : i64
    %56 = llvm.mlir.constant(1 : i64) : i64
    %57 = llvm.alloca %56 x i64 : (i64) -> !llvm.ptr
    llvm.store %55, %57 : i64, !llvm.ptr
    %58 = arith.constant 0 : i32
    %59 = arith.extsi %58 : i32 to i64
    %60 = llvm.mlir.constant(1 : i64) : i64
    %61 = llvm.alloca %60 x i64 : (i64) -> !llvm.ptr
    llvm.store %59, %61 : i64, !llvm.ptr
    cf.br ^bb12
    ^bb12:
    %62 = llvm.load %57 : !llvm.ptr -> i64
    %63 = arith.constant 0 : i32
    %65 = arith.extsi %63 : i32 to i64
    %64 = arith.cmpi sgt, %62, %65 : i64
    cf.cond_br %64, ^bb13, ^bb14
    ^bb13:
      %66 = llvm.load %57 : !llvm.ptr -> i64
      %67 = arith.constant 2 : i32
      %69 = arith.extsi %67 : i32 to i64
      %68 = arith.remsi %66, %69 : i64
      %70 = arith.constant 1 : i32
      %72 = arith.extsi %70 : i32 to i64
      %71 = arith.cmpi eq, %68, %72 : i64
      cf.cond_br %71, ^bb15, ^bb16
      ^bb15:
        %73 = llvm.load %61 : !llvm.ptr -> i64
        %74 = llvm.load %54 : !llvm.ptr -> i64
        %75 = arith.addi %73, %74 : i64
        %76 = arith.remsi %75, %arg2 : i64
        llvm.store %76, %61 : i64, !llvm.ptr
        cf.br ^bb17
      ^bb16:
        cf.br ^bb17
      ^bb17:
      %77 = llvm.load %54 : !llvm.ptr -> i64
      %78 = arith.constant 2 : i32
      %80 = arith.extsi %78 : i32 to i64
      %79 = arith.muli %77, %80 : i64
      %81 = arith.remsi %79, %arg2 : i64
      llvm.store %81, %54 : i64, !llvm.ptr
      %82 = llvm.load %57 : !llvm.ptr -> i64
      %83 = arith.constant 2 : i32
      %85 = arith.extsi %83 : i32 to i64
      %84 = arith.divsi %82, %85 : i64
      llvm.store %84, %57 : i64, !llvm.ptr
      cf.br ^bb12
    ^bb14:
    %86 = llvm.load %61 : !llvm.ptr -> i64
    func.return %86 : i64
  }
  func.func @mod_pow(%arg0: i64, %arg1: i64, %arg2: i64) -> i64 {
    %87 = arith.constant 1 : i32
    %89 = arith.extsi %87 : i32 to i64
    %88 = arith.cmpi eq, %arg2, %89 : i64
    cf.cond_br %88, ^bb18, ^bb19
    ^bb18:
      %90 = arith.constant 0 : i32
      %91 = arith.extsi %90 : i32 to i64
      func.return %91 : i64
    ^bb19:
      cf.br ^bb20
    ^bb20:
    %92 = arith.constant 1 : i32
    %93 = arith.extsi %92 : i32 to i64
    %94 = llvm.mlir.constant(1 : i64) : i64
    %95 = llvm.alloca %94 x i64 : (i64) -> !llvm.ptr
    llvm.store %93, %95 : i64, !llvm.ptr
    %96 = arith.remsi %arg0, %arg2 : i64
    %97 = llvm.mlir.constant(1 : i64) : i64
    %98 = llvm.alloca %97 x i64 : (i64) -> !llvm.ptr
    llvm.store %96, %98 : i64, !llvm.ptr
    %99 = llvm.mlir.constant(1 : i64) : i64
    %100 = llvm.alloca %99 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg1, %100 : i64, !llvm.ptr
    cf.br ^bb21
    ^bb21:
    %101 = llvm.load %100 : !llvm.ptr -> i64
    %102 = arith.constant 0 : i32
    %104 = arith.extsi %102 : i32 to i64
    %103 = arith.cmpi sgt, %101, %104 : i64
    cf.cond_br %103, ^bb22, ^bb23
    ^bb22:
      %105 = llvm.load %100 : !llvm.ptr -> i64
      %106 = arith.constant 2 : i32
      %108 = arith.extsi %106 : i32 to i64
      %107 = arith.remsi %105, %108 : i64
      %109 = arith.constant 1 : i32
      %111 = arith.extsi %109 : i32 to i64
      %110 = arith.cmpi eq, %107, %111 : i64
      cf.cond_br %110, ^bb24, ^bb25
      ^bb24:
        %113 = llvm.load %95 : !llvm.ptr -> i64
        %114 = llvm.load %98 : !llvm.ptr -> i64
        %112 = func.call @mulmod(%113, %114, %arg2) : (i64, i64, i64) -> i64
        llvm.store %112, %95 : i64, !llvm.ptr
        cf.br ^bb26
      ^bb25:
        cf.br ^bb26
      ^bb26:
      %116 = llvm.load %98 : !llvm.ptr -> i64
      %117 = llvm.load %98 : !llvm.ptr -> i64
      %115 = func.call @mulmod(%116, %117, %arg2) : (i64, i64, i64) -> i64
      llvm.store %115, %98 : i64, !llvm.ptr
      %118 = llvm.load %100 : !llvm.ptr -> i64
      %119 = arith.constant 2 : i32
      %121 = arith.extsi %119 : i32 to i64
      %120 = arith.divsi %118, %121 : i64
      llvm.store %120, %100 : i64, !llvm.ptr
      cf.br ^bb21
    ^bb23:
    %122 = llvm.load %95 : !llvm.ptr -> i64
    func.return %122 : i64
  }
  func.func @is_prime(%arg0: i64) -> i1 {
    %123 = arith.constant 2 : i32
    %125 = arith.extsi %123 : i32 to i64
    %124 = arith.cmpi slt, %arg0, %125 : i64
    cf.cond_br %124, ^bb27, ^bb28
    ^bb27:
      %126 = arith.constant 0 : i1
      func.return %126 : i1
    ^bb28:
      cf.br ^bb29
    ^bb29:
    %127 = arith.constant 4 : i32
    %129 = arith.extsi %127 : i32 to i64
    %128 = arith.cmpi slt, %arg0, %129 : i64
    cf.cond_br %128, ^bb30, ^bb31
    ^bb30:
      %130 = arith.constant 1 : i1
      func.return %130 : i1
    ^bb31:
      cf.br ^bb32
    ^bb32:
    %131 = arith.constant 2 : i32
    %133 = arith.extsi %131 : i32 to i64
    %132 = arith.remsi %arg0, %133 : i64
    %134 = arith.constant 0 : i32
    %136 = arith.extsi %134 : i32 to i64
    %135 = arith.cmpi eq, %132, %136 : i64
    %137 = scf.if %135 -> (i1) {
      %138 = arith.constant true
      scf.yield %138 : i1
    } else {
      %139 = arith.constant 3 : i32
      %141 = arith.extsi %139 : i32 to i64
      %140 = arith.remsi %arg0, %141 : i64
      %142 = arith.constant 0 : i32
      %144 = arith.extsi %142 : i32 to i64
      %143 = arith.cmpi eq, %140, %144 : i64
      scf.yield %143 : i1
    }
    cf.cond_br %137, ^bb33, ^bb34
    ^bb33:
      %145 = arith.constant 0 : i1
      func.return %145 : i1
    ^bb34:
      cf.br ^bb35
    ^bb35:
    %146 = arith.constant 5 : i32
    %147 = arith.extsi %146 : i32 to i64
    %148 = llvm.mlir.constant(1 : i64) : i64
    %149 = llvm.alloca %148 x i64 : (i64) -> !llvm.ptr
    llvm.store %147, %149 : i64, !llvm.ptr
    cf.br ^bb36
    ^bb36:
    %150 = llvm.load %149 : !llvm.ptr -> i64
    %151 = llvm.load %149 : !llvm.ptr -> i64
    %152 = arith.muli %150, %151 : i64
    %153 = arith.cmpi sle, %152, %arg0 : i64
    cf.cond_br %153, ^bb37, ^bb38
    ^bb37:
      %154 = llvm.load %149 : !llvm.ptr -> i64
      %155 = arith.remsi %arg0, %154 : i64
      %156 = arith.constant 0 : i32
      %158 = arith.extsi %156 : i32 to i64
      %157 = arith.cmpi eq, %155, %158 : i64
      %159 = scf.if %157 -> (i1) {
        %160 = arith.constant true
        scf.yield %160 : i1
      } else {
        %161 = llvm.load %149 : !llvm.ptr -> i64
        %162 = arith.constant 2 : i32
        %164 = arith.extsi %162 : i32 to i64
        %163 = arith.addi %161, %164 : i64
        %165 = arith.remsi %arg0, %163 : i64
        %166 = arith.constant 0 : i32
        %168 = arith.extsi %166 : i32 to i64
        %167 = arith.cmpi eq, %165, %168 : i64
        scf.yield %167 : i1
      }
      cf.cond_br %159, ^bb39, ^bb40
      ^bb39:
        %169 = arith.constant 0 : i1
        func.return %169 : i1
      ^bb40:
        cf.br ^bb41
      ^bb41:
      %170 = llvm.load %149 : !llvm.ptr -> i64
      %171 = arith.constant 6 : i32
      %173 = arith.extsi %171 : i32 to i64
      %172 = arith.addi %170, %173 : i64
      llvm.store %172, %149 : i64, !llvm.ptr
      cf.br ^bb36
    ^bb38:
    %174 = arith.constant 1 : i1
    func.return %174 : i1
  }
  func.func private @calloc(i64, i64) -> !llvm.ptr
  func.func private @free(!llvm.ptr) -> ()
  func.func @main() -> i32 {
    %175 = arith.constant 1500000 : i32
    %176 = arith.extsi %175 : i32 to i64
    %178 = arith.constant 1 : i32
    %180 = arith.extsi %178 : i32 to i64
    %179 = arith.addi %176, %180 : i64
    %181 = arith.constant 4 : i32
    %182 = arith.extsi %181 : i32 to i64
    %177 = func.call @calloc(%179, %182) : (i64, i64) -> !llvm.ptr
    %183 = llvm.mlir.zero : !llvm.ptr
    %184 = llvm.icmp "eq" %177, %183 : !llvm.ptr
    cf.cond_br %184, ^bb42, ^bb43
    ^bb42:
      %185 = arith.constant 1 : i32
      func.return %185 : i32
    ^bb43:
      cf.br ^bb44
    ^bb44:
    %186 = arith.constant 2 : i32
    %187 = arith.extsi %186 : i32 to i64
    %188 = llvm.mlir.constant(1 : i64) : i64
    %189 = llvm.alloca %188 x i64 : (i64) -> !llvm.ptr
    llvm.store %187, %189 : i64, !llvm.ptr
    cf.br ^bb45
    ^bb45:
    %190 = arith.constant 2 : i32
    %191 = llvm.load %189 : !llvm.ptr -> i64
    %193 = arith.extsi %190 : i32 to i64
    %192 = arith.muli %193, %191 : i64
    %194 = llvm.load %189 : !llvm.ptr -> i64
    %195 = arith.constant 1 : i32
    %197 = arith.extsi %195 : i32 to i64
    %196 = arith.addi %194, %197 : i64
    %198 = arith.muli %192, %196 : i64
    %199 = arith.cmpi sle, %198, %176 : i64
    cf.cond_br %199, ^bb46, ^bb47
    ^bb46:
      %200 = arith.constant 1 : i32
      %201 = llvm.load %189 : !llvm.ptr -> i64
      %202 = arith.constant 2 : i32
      %204 = arith.extsi %202 : i32 to i64
      %203 = arith.remsi %201, %204 : i64
      %206 = arith.extsi %200 : i32 to i64
      %205 = arith.addi %206, %203 : i64
      %207 = llvm.mlir.constant(1 : i64) : i64
      %208 = llvm.alloca %207 x i64 : (i64) -> !llvm.ptr
      llvm.store %205, %208 : i64, !llvm.ptr
      cf.br ^bb48
      ^bb48:
      %209 = llvm.load %208 : !llvm.ptr -> i64
      %210 = llvm.load %189 : !llvm.ptr -> i64
      %211 = arith.cmpi slt, %209, %210 : i64
      cf.cond_br %211, ^bb49, ^bb50
      ^bb49:
        %213 = llvm.load %189 : !llvm.ptr -> i64
        %214 = llvm.load %208 : !llvm.ptr -> i64
        %212 = func.call @gcd(%213, %214) : (i64, i64) -> i64
        %215 = arith.constant 1 : i32
        %217 = arith.extsi %215 : i32 to i64
        %216 = arith.cmpi eq, %212, %217 : i64
        cf.cond_br %216, ^bb51, ^bb52
        ^bb51:
          %218 = llvm.load %189 : !llvm.ptr -> i64
          %219 = llvm.load %189 : !llvm.ptr -> i64
          %220 = arith.muli %218, %219 : i64
          %221 = llvm.load %208 : !llvm.ptr -> i64
          %222 = llvm.load %208 : !llvm.ptr -> i64
          %223 = arith.muli %221, %222 : i64
          %224 = arith.subi %220, %223 : i64
          %225 = arith.constant 2 : i32
          %226 = llvm.load %189 : !llvm.ptr -> i64
          %228 = arith.extsi %225 : i32 to i64
          %227 = arith.muli %228, %226 : i64
          %229 = llvm.load %208 : !llvm.ptr -> i64
          %230 = arith.muli %227, %229 : i64
          %231 = llvm.load %189 : !llvm.ptr -> i64
          %232 = llvm.load %189 : !llvm.ptr -> i64
          %233 = arith.muli %231, %232 : i64
          %234 = llvm.load %208 : !llvm.ptr -> i64
          %235 = llvm.load %208 : !llvm.ptr -> i64
          %236 = arith.muli %234, %235 : i64
          %237 = arith.addi %233, %236 : i64
          %238 = arith.addi %224, %230 : i64
          %239 = arith.addi %238, %237 : i64
          %240 = llvm.mlir.constant(1 : i64) : i64
          %241 = llvm.alloca %240 x i64 : (i64) -> !llvm.ptr
          llvm.store %239, %241 : i64, !llvm.ptr
          cf.br ^bb54
          ^bb54:
          %242 = llvm.load %241 : !llvm.ptr -> i64
          %243 = arith.cmpi sle, %242, %176 : i64
          cf.cond_br %243, ^bb55, ^bb56
          ^bb55:
            %245 = llvm.load %241 : !llvm.ptr -> i64
            %246 = arith.trunci %245 : i64 to i32
            %247 = arith.extsi %246 : i32 to i64
            %248 = llvm.getelementptr %177[%247] : (!llvm.ptr, i64) -> !llvm.ptr, i32
            %244 = llvm.load %248 : !llvm.ptr -> i32
            %249 = arith.constant 1 : i32
            %250 = arith.addi %244, %249 : i32
            %251 = llvm.load %241 : !llvm.ptr -> i64
            %252 = arith.trunci %251 : i64 to i32
            %253 = arith.extsi %252 : i32 to i64
            %254 = llvm.getelementptr %177[%253] : (!llvm.ptr, i64) -> !llvm.ptr, i32
            llvm.store %250, %254 : i32, !llvm.ptr
            %255 = llvm.load %241 : !llvm.ptr -> i64
            %256 = arith.addi %255, %239 : i64
            llvm.store %256, %241 : i64, !llvm.ptr
            cf.br ^bb54
          ^bb56:
          cf.br ^bb53
        ^bb52:
          cf.br ^bb53
        ^bb53:
        %257 = llvm.load %208 : !llvm.ptr -> i64
        %258 = arith.constant 2 : i32
        %260 = arith.extsi %258 : i32 to i64
        %259 = arith.addi %257, %260 : i64
        llvm.store %259, %208 : i64, !llvm.ptr
        cf.br ^bb48
      ^bb50:
      %261 = llvm.load %189 : !llvm.ptr -> i64
      %262 = arith.constant 1 : i32
      %264 = arith.extsi %262 : i32 to i64
      %263 = arith.addi %261, %264 : i64
      llvm.store %263, %189 : i64, !llvm.ptr
      cf.br ^bb45
    ^bb47:
    %265 = arith.constant 0 : i32
    %266 = arith.extsi %265 : i32 to i64
    %267 = llvm.mlir.constant(1 : i64) : i64
    %268 = llvm.alloca %267 x i64 : (i64) -> !llvm.ptr
    llvm.store %266, %268 : i64, !llvm.ptr
    %269 = arith.constant 1 : i32
    %270 = arith.constant 1 : i32
    %272 = arith.extsi %270 : i32 to i64
    %271 = arith.addi %176, %272 : i64
    %273 = arith.index_cast %269 : i32 to index
    %274 = arith.index_cast %271 : i32 to index
    %276 = arith.constant 1 : index
    %277 = arith.constant -1 : index
    %278 = arith.cmpi sle, %273, %274 : index
    %275 = arith.select %278, %276, %277 : index
    cf.br ^bb57(%273 : index)
    ^bb57(%279: index):
    %280 = arith.cmpi slt, %279, %274 : index
    %281 = arith.cmpi sgt, %279, %274 : index
    %282 = arith.select %278, %280, %281 : i1
    cf.cond_br %282, ^bb58(%279 : index), ^bb59(%279 : index)
    ^bb58(%283: index):
      %285 = arith.index_cast %283 : index to i32
      %286 = arith.extsi %285 : i32 to i64
      %287 = llvm.getelementptr %177[%286] : (!llvm.ptr, i64) -> !llvm.ptr, i32
      %284 = llvm.load %287 : !llvm.ptr -> i32
      %288 = arith.constant 1 : i32
      %289 = arith.cmpi eq, %284, %288 : i32
      cf.cond_br %289, ^bb60, ^bb61
      ^bb60:
        %290 = llvm.load %268 : !llvm.ptr -> i64
        %291 = arith.constant 1 : i32
        %293 = arith.extsi %291 : i32 to i64
        %292 = arith.addi %290, %293 : i64
        llvm.store %292, %268 : i64, !llvm.ptr
        cf.br ^bb62
      ^bb61:
        cf.br ^bb62
      ^bb62:
      %294 = arith.addi %283, %275 : index
      cf.br ^bb57(%294 : index)
    ^bb59(%295: index):
    %296 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %297 = llvm.load %268 : !llvm.ptr -> i64
    %298 = llvm.call @printf(%296, %297) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%177) : (!llvm.ptr) -> ()
    %300 = arith.constant 0 : i32
    func.return %300 : i32
  }
}