Problem 498

Remainder of Polynomial Division — C(n,m,d)=C(n,d)*C(n-d-1,m-d-1) via Lucas.

View problem on Project Euler

Performance comparison

Flow source

# Project Euler 498
# Remainder of Polynomial Division — C(n,m,d)=C(n,d)*C(n-d-1,m-d-1) via Lucas.

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

function modpow(base0: i64, exp0: i64, mod: i64) -> i64 {
    let mut r: i64 = 1
    let mut b: i64 = base0 % mod
    let mut e: i64 = exp0
    while e > 0 {
        if e % 2 == 1 {
            let t: i128 = (r as i128) * (b as i128) % (mod as i128)
            r = t as i64
        }
        let t2: i128 = (b as i128) * (b as i128) % (mod as i128)
        b = t2 as i64
        e = e / 2
    }
    return r
}

function nCk_small(nn: i64, kk: i64, fact: ptr<i64>, invfact: ptr<i64>, p: i64) -> i64 {
    if kk < 0 || kk > nn { return 0 }
    return ((fact[nn] * invfact[kk]) % p) * invfact[nn - kk] % p
}

function nCk_lucas(nn0: i64, kk0: i64, fact: ptr<i64>, invfact: ptr<i64>, p: i64) -> i64 {
    let mut nn: i64 = nn0
    let mut kk: i64 = kk0
    let mut res: i64 = 1
    while nn > 0 || kk > 0 {
        let ni: i64 = nn % p
        let ki: i64 = kk % p
        if ki > ni { return 0 }
        res = (res * nCk_small(ni, ki, fact, invfact, p)) % p
        nn = nn / p
        kk = kk / p
    }
    return res
}

function main() -> i32 {
    let n: i64 = 10000000000000
    let m: i64 = 1000000000000
    let d: i64 = 10000
    let p: i64 = 999999937
    # max Lucas digit for these params is n%p = 630000
    let max_digit: i64 = 630000
    let fact: ptr<i64> = calloc(max_digit + 1, 8)
    let invfact: ptr<i64> = calloc(max_digit + 1, 8)
    if fact == null || invfact == null { return 1 }
    fact[0] = 1
    let mut i: i64 = 1
    while i <= max_digit {
        fact[i] = (fact[i - 1] * i) % p
        i = i + 1
    }
    invfact[max_digit] = modpow(fact[max_digit], p - 2, p)
    i = max_digit
    while i > 0 {
        invfact[i - 1] = (invfact[i] * i) % p
        i = i - 1
    }
    let part1: i64 = nCk_lucas(n, d, fact, invfact, p)
    let part2: i64 = nCk_lucas(n - d - 1, m - d - 1, fact, invfact, p)
    printf("%lld\n", (part1 * part2) % p)
    free(invfact)
    free(fact)
    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 modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod);
int64_t nCk_small_i64_i64_ptr_i64_ptr_i64_i64(int64_t nn, int64_t kk, int64_t* fact, int64_t* invfact, int64_t p);
int64_t nCk_lucas_i64_i64_ptr_i64_ptr_i64_i64(int64_t nn0, int64_t kk0, int64_t* fact, int64_t* invfact, int64_t p);
int32_t main(void);



int64_t modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod) {
    int64_t r = 1;
    int64_t b = FLOW_CHECKED_MOD((base0), (mod));
    int64_t e = exp0;
    while (e > 0) {
        if (FLOW_CHECKED_MOD((e), (2)) == 1) {
            __int128 t = FLOW_CHECKED_MOD(((((__int128)(r)) * ((__int128)(b)))), (((__int128)(mod))));
            r = ((int64_t)(t));
        }
        __int128 t2 = FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(b)))), (((__int128)(mod))));
        b = ((int64_t)(t2));
        e = FLOW_CHECKED_DIV((e), (2));
    }
    return r;
}

int64_t nCk_small_i64_i64_ptr_i64_ptr_i64_i64(int64_t nn, int64_t kk, int64_t* fact, int64_t* invfact, int64_t p) {
    if ((kk < 0 || kk > nn)) {
        return 0;
    }
    return FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD(((fact[nn] * invfact[kk])), (p)) * invfact[(nn - kk)])), (p));
}

int64_t nCk_lucas_i64_i64_ptr_i64_ptr_i64_i64(int64_t nn0, int64_t kk0, int64_t* fact, int64_t* invfact, int64_t p) {
    int64_t nn = nn0;
    int64_t kk = kk0;
    int64_t res = 1;
    while ((nn > 0 || kk > 0)) {
        int64_t ni = FLOW_CHECKED_MOD((nn), (p));
        int64_t ki = FLOW_CHECKED_MOD((kk), (p));
        if (ki > ni) {
            return 0;
        }
        res = FLOW_CHECKED_MOD(((res * nCk_small_i64_i64_ptr_i64_ptr_i64_i64(ni, ki, fact, invfact, p))), (p));
        nn = FLOW_CHECKED_DIV((nn), (p));
        kk = FLOW_CHECKED_DIV((kk), (p));
    }
    return res;
}

int32_t main(void) {
    int64_t n = 10000000000000;
    int64_t m = 1000000000000;
    int64_t d = 10000;
    int64_t p = 999999937;
    int64_t max_digit = 630000;
    int64_t* fact = (int64_t*)(calloc((max_digit + 1), 8));
    int64_t* invfact = (int64_t*)(calloc((max_digit + 1), 8));
    if ((fact == NULL || invfact == NULL)) {
        return 1;
    }
    fact[0] = 1;
    int64_t i = 1;
    while (i <= max_digit) {
        fact[i] = FLOW_CHECKED_MOD(((fact[(i - 1)] * i)), (p));
        i = (i + 1);
    }
    invfact[max_digit] = modpow_i64_i64_i64(fact[max_digit], (p - 2), p);
    i = max_digit;
    while (i > 0) {
        invfact[(i - 1)] = FLOW_CHECKED_MOD(((invfact[i] * i)), (p));
        i = (i - 1);
    }
    int64_t part1 = nCk_lucas_i64_i64_ptr_i64_ptr_i64_i64(n, d, fact, invfact, p);
    int64_t part2 = nCk_lucas_i64_i64_ptr_i64_ptr_i64_i64(((n - d) - 1), ((m - d) - 1), fact, invfact, p);
    printf("%lld\n", FLOW_CHECKED_MOD(((part1 * part2)), (p)));
    free(invfact);
    free(fact);
    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 @modpow(%arg0: i64, %arg1: i64, %arg2: i64) -> i64 {
    %0 = arith.constant 1 : i32
    %1 = arith.extsi %0 : i32 to i64
    %2 = llvm.mlir.constant(1 : i64) : i64
    %3 = llvm.alloca %2 x i64 : (i64) -> !llvm.ptr
    llvm.store %1, %3 : i64, !llvm.ptr
    %4 = arith.remsi %arg0, %arg2 : i64
    %5 = llvm.mlir.constant(1 : i64) : i64
    %6 = llvm.alloca %5 x i64 : (i64) -> !llvm.ptr
    llvm.store %4, %6 : i64, !llvm.ptr
    %7 = llvm.mlir.constant(1 : i64) : i64
    %8 = llvm.alloca %7 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg1, %8 : i64, !llvm.ptr
    cf.br ^bb0
    ^bb0:
    %9 = llvm.load %8 : !llvm.ptr -> i64
    %10 = arith.constant 0 : i32
    %12 = arith.extsi %10 : i32 to i64
    %11 = arith.cmpi sgt, %9, %12 : i64
    cf.cond_br %11, ^bb1, ^bb2
    ^bb1:
      %13 = llvm.load %8 : !llvm.ptr -> i64
      %14 = arith.constant 2 : i32
      %16 = arith.extsi %14 : i32 to i64
      %15 = arith.remsi %13, %16 : i64
      %17 = arith.constant 1 : i32
      %19 = arith.extsi %17 : i32 to i64
      %18 = arith.cmpi eq, %15, %19 : i64
      cf.cond_br %18, ^bb3, ^bb4
      ^bb3:
        %20 = llvm.load %3 : !llvm.ptr -> i64
        %21 = arith.extsi %20 : i64 to i128
        %22 = llvm.load %6 : !llvm.ptr -> i64
        %23 = arith.extsi %22 : i64 to i128
        %25 = arith.trunci %21 : i128 to i64
        %26 = arith.trunci %23 : i128 to i64
        %24 = arith.muli %25, %26 : i64
        %27 = arith.extsi %arg2 : i64 to i128
        %29 = arith.trunci %27 : i128 to i64
        %28 = arith.remsi %24, %29 : i64
        %30 = arith.extsi %28 : i64 to i128
        %31 = arith.trunci %30 : i128 to i64
        llvm.store %31, %3 : i64, !llvm.ptr
        cf.br ^bb5
      ^bb4:
        cf.br ^bb5
      ^bb5:
      %32 = llvm.load %6 : !llvm.ptr -> i64
      %33 = arith.extsi %32 : i64 to i128
      %34 = llvm.load %6 : !llvm.ptr -> i64
      %35 = arith.extsi %34 : i64 to i128
      %37 = arith.trunci %33 : i128 to i64
      %38 = arith.trunci %35 : i128 to i64
      %36 = arith.muli %37, %38 : i64
      %39 = arith.extsi %arg2 : i64 to i128
      %41 = arith.trunci %39 : i128 to i64
      %40 = arith.remsi %36, %41 : i64
      %42 = arith.extsi %40 : i64 to i128
      %43 = arith.trunci %42 : i128 to i64
      llvm.store %43, %6 : i64, !llvm.ptr
      %44 = llvm.load %8 : !llvm.ptr -> i64
      %45 = arith.constant 2 : i32
      %47 = arith.extsi %45 : i32 to i64
      %46 = arith.divsi %44, %47 : i64
      llvm.store %46, %8 : i64, !llvm.ptr
      cf.br ^bb0
    ^bb2:
    %48 = llvm.load %3 : !llvm.ptr -> i64
    func.return %48 : i64
  }
  func.func @nCk_small(%arg0: i64, %arg1: i64, %arg2: !llvm.ptr, %arg3: !llvm.ptr, %arg4: i64) -> i64 {
    %49 = arith.constant 0 : i32
    %51 = arith.extsi %49 : i32 to i64
    %50 = arith.cmpi slt, %arg1, %51 : i64
    %52 = scf.if %50 -> (i1) {
      %53 = arith.constant true
      scf.yield %53 : i1
    } else {
      %54 = arith.cmpi sgt, %arg1, %arg0 : i64
      scf.yield %54 : i1
    }
    cf.cond_br %52, ^bb6, ^bb7
    ^bb6:
      %55 = arith.constant 0 : i32
      %56 = arith.extsi %55 : i32 to i64
      func.return %56 : i64
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %58 = llvm.getelementptr %arg2[%arg0] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    %57 = llvm.load %58 : !llvm.ptr -> i64
    %60 = llvm.getelementptr %arg3[%arg1] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    %59 = llvm.load %60 : !llvm.ptr -> i64
    %61 = arith.muli %57, %59 : i64
    %62 = arith.remsi %61, %arg4 : i64
    %64 = arith.subi %arg0, %arg1 : i64
    %65 = llvm.getelementptr %arg3[%64] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    %63 = llvm.load %65 : !llvm.ptr -> i64
    %66 = arith.muli %62, %63 : i64
    %67 = arith.remsi %66, %arg4 : i64
    func.return %67 : i64
  }
  func.func @nCk_lucas(%arg0: i64, %arg1: i64, %arg2: !llvm.ptr, %arg3: !llvm.ptr, %arg4: i64) -> i64 {
    %68 = llvm.mlir.constant(1 : i64) : i64
    %69 = llvm.alloca %68 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg0, %69 : i64, !llvm.ptr
    %70 = llvm.mlir.constant(1 : i64) : i64
    %71 = llvm.alloca %70 x i64 : (i64) -> !llvm.ptr
    llvm.store %arg1, %71 : i64, !llvm.ptr
    %72 = arith.constant 1 : i32
    %73 = arith.extsi %72 : i32 to i64
    %74 = llvm.mlir.constant(1 : i64) : i64
    %75 = llvm.alloca %74 x i64 : (i64) -> !llvm.ptr
    llvm.store %73, %75 : i64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %76 = llvm.load %69 : !llvm.ptr -> i64
    %77 = arith.constant 0 : i32
    %79 = arith.extsi %77 : i32 to i64
    %78 = arith.cmpi sgt, %76, %79 : i64
    %80 = scf.if %78 -> (i1) {
      %81 = arith.constant true
      scf.yield %81 : i1
    } else {
      %82 = llvm.load %71 : !llvm.ptr -> i64
      %83 = arith.constant 0 : i32
      %85 = arith.extsi %83 : i32 to i64
      %84 = arith.cmpi sgt, %82, %85 : i64
      scf.yield %84 : i1
    }
    cf.cond_br %80, ^bb10, ^bb11
    ^bb10:
      %86 = llvm.load %69 : !llvm.ptr -> i64
      %87 = arith.remsi %86, %arg4 : i64
      %88 = llvm.load %71 : !llvm.ptr -> i64
      %89 = arith.remsi %88, %arg4 : i64
      %90 = arith.cmpi sgt, %89, %87 : i64
      cf.cond_br %90, ^bb12, ^bb13
      ^bb12:
        %91 = arith.constant 0 : i32
        %92 = arith.extsi %91 : i32 to i64
        func.return %92 : i64
      ^bb13:
        cf.br ^bb14
      ^bb14:
      %93 = llvm.load %75 : !llvm.ptr -> i64
      %94 = func.call @nCk_small(%87, %89, %arg2, %arg3, %arg4) : (i64, i64, !llvm.ptr, !llvm.ptr, i64) -> i64
      %95 = arith.muli %93, %94 : i64
      %96 = arith.remsi %95, %arg4 : i64
      llvm.store %96, %75 : i64, !llvm.ptr
      %97 = llvm.load %69 : !llvm.ptr -> i64
      %98 = arith.divsi %97, %arg4 : i64
      llvm.store %98, %69 : i64, !llvm.ptr
      %99 = llvm.load %71 : !llvm.ptr -> i64
      %100 = arith.divsi %99, %arg4 : i64
      llvm.store %100, %71 : i64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %101 = llvm.load %75 : !llvm.ptr -> i64
    func.return %101 : i64
  }
  func.func @main() -> i32 {
    %102 = arith.constant 9995705032704 : i32
    %103 = arith.extsi %102 : i32 to i64
    %104 = arith.constant 995705032704 : i32
    %105 = arith.extsi %104 : i32 to i64
    %106 = arith.constant 10000 : i32
    %107 = arith.extsi %106 : i32 to i64
    %108 = arith.constant 999999937 : i32
    %109 = arith.extsi %108 : i32 to i64
    %110 = arith.constant 630000 : i32
    %111 = arith.extsi %110 : i32 to i64
    %113 = arith.constant 1 : i32
    %115 = arith.extsi %113 : i32 to i64
    %114 = arith.addi %111, %115 : i64
    %116 = arith.constant 8 : i32
    %117 = arith.extsi %116 : i32 to i64
    %112 = func.call @calloc(%114, %117) : (i64, i64) -> !llvm.ptr
    %119 = arith.constant 1 : i32
    %121 = arith.extsi %119 : i32 to i64
    %120 = arith.addi %111, %121 : i64
    %122 = arith.constant 8 : i32
    %123 = arith.extsi %122 : i32 to i64
    %118 = func.call @calloc(%120, %123) : (i64, i64) -> !llvm.ptr
    %124 = llvm.mlir.zero : !llvm.ptr
    %125 = llvm.icmp "eq" %112, %124 : !llvm.ptr
    %126 = scf.if %125 -> (i1) {
      %127 = arith.constant true
      scf.yield %127 : i1
    } else {
      %128 = llvm.mlir.zero : !llvm.ptr
      %129 = llvm.icmp "eq" %118, %128 : !llvm.ptr
      scf.yield %129 : i1
    }
    cf.cond_br %126, ^bb15, ^bb16
    ^bb15:
      %130 = arith.constant 1 : i32
      func.return %130 : i32
    ^bb16:
      cf.br ^bb17
    ^bb17:
    %131 = arith.constant 1 : i32
    %132 = arith.constant 0 : i32
    %133 = arith.extsi %131 : i32 to i64
    %134 = arith.extsi %132 : i32 to i64
    %135 = llvm.getelementptr %112[%134] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %133, %135 : i64, !llvm.ptr
    %136 = arith.constant 1 : i32
    %137 = arith.extsi %136 : i32 to i64
    %138 = llvm.mlir.constant(1 : i64) : i64
    %139 = llvm.alloca %138 x i64 : (i64) -> !llvm.ptr
    llvm.store %137, %139 : i64, !llvm.ptr
    cf.br ^bb18
    ^bb18:
    %140 = llvm.load %139 : !llvm.ptr -> i64
    %141 = arith.cmpi sle, %140, %111 : i64
    cf.cond_br %141, ^bb19, ^bb20
    ^bb19:
      %143 = llvm.load %139 : !llvm.ptr -> i64
      %144 = arith.constant 1 : i32
      %146 = arith.extsi %144 : i32 to i64
      %145 = arith.subi %143, %146 : i64
      %147 = llvm.getelementptr %112[%145] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %142 = llvm.load %147 : !llvm.ptr -> i64
      %148 = llvm.load %139 : !llvm.ptr -> i64
      %149 = arith.muli %142, %148 : i64
      %150 = arith.remsi %149, %109 : i64
      %151 = llvm.load %139 : !llvm.ptr -> i64
      %152 = llvm.getelementptr %112[%151] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %150, %152 : i64, !llvm.ptr
      %153 = llvm.load %139 : !llvm.ptr -> i64
      %154 = arith.constant 1 : i32
      %156 = arith.extsi %154 : i32 to i64
      %155 = arith.addi %153, %156 : i64
      llvm.store %155, %139 : i64, !llvm.ptr
      cf.br ^bb18
    ^bb20:
    %159 = llvm.getelementptr %112[%111] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    %158 = llvm.load %159 : !llvm.ptr -> i64
    %160 = arith.constant 2 : i32
    %162 = arith.extsi %160 : i32 to i64
    %161 = arith.subi %109, %162 : i64
    %157 = func.call @modpow(%158, %161, %109) : (i64, i64, i64) -> i64
    %163 = llvm.getelementptr %118[%111] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %157, %163 : i64, !llvm.ptr
    llvm.store %111, %139 : i64, !llvm.ptr
    cf.br ^bb21
    ^bb21:
    %164 = llvm.load %139 : !llvm.ptr -> i64
    %165 = arith.constant 0 : i32
    %167 = arith.extsi %165 : i32 to i64
    %166 = arith.cmpi sgt, %164, %167 : i64
    cf.cond_br %166, ^bb22, ^bb23
    ^bb22:
      %169 = llvm.load %139 : !llvm.ptr -> i64
      %170 = llvm.getelementptr %118[%169] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %168 = llvm.load %170 : !llvm.ptr -> i64
      %171 = llvm.load %139 : !llvm.ptr -> i64
      %172 = arith.muli %168, %171 : i64
      %173 = arith.remsi %172, %109 : i64
      %174 = llvm.load %139 : !llvm.ptr -> i64
      %175 = arith.constant 1 : i32
      %177 = arith.extsi %175 : i32 to i64
      %176 = arith.subi %174, %177 : i64
      %178 = llvm.getelementptr %118[%176] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %173, %178 : i64, !llvm.ptr
      %179 = llvm.load %139 : !llvm.ptr -> i64
      %180 = arith.constant 1 : i32
      %182 = arith.extsi %180 : i32 to i64
      %181 = arith.subi %179, %182 : i64
      llvm.store %181, %139 : i64, !llvm.ptr
      cf.br ^bb21
    ^bb23:
    %183 = func.call @nCk_lucas(%103, %107, %112, %118, %109) : (i64, i64, !llvm.ptr, !llvm.ptr, i64) -> i64
    %185 = arith.subi %103, %107 : i64
    %186 = arith.constant 1 : i32
    %188 = arith.extsi %186 : i32 to i64
    %187 = arith.subi %185, %188 : i64
    %189 = arith.subi %105, %107 : i64
    %190 = arith.constant 1 : i32
    %192 = arith.extsi %190 : i32 to i64
    %191 = arith.subi %189, %192 : i64
    %184 = func.call @nCk_lucas(%187, %191, %112, %118, %109) : (i64, i64, !llvm.ptr, !llvm.ptr, i64) -> i64
    %193 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %194 = arith.muli %183, %184 : i64
    %195 = arith.remsi %194, %109 : i64
    %196 = llvm.call @printf(%193, %195) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%118) : (!llvm.ptr) -> ()
    func.call @free(%112) : (!llvm.ptr) -> ()
    %199 = arith.constant 0 : i32
    func.return %199 : i32
  }
}