# Project Euler 330
# (A(10^9)+B(10^9)) mod 77777777 via CRT over prime factors.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function modpow(base: i64, exp: i64, mod: i64) -> i64 {
let mut r: i64 = 1
let mut b: i64 = ((base % mod) + mod) % mod
let mut e: i64 = exp
while e > 0 {
if e % 2 == 1 { r = (r * b) % mod }
b = (b * b) % mod
e = e / 2
}
return r
}
function comb_small(n: i64, k0: i64, p: i64) -> i64 {
if k0 < 0 || k0 > n { return 0 }
if k0 == 0 || k0 == n { return 1 }
let mut k: i64 = k0
if k > n - k { k = n - k }
let mut num: i64 = 1
let mut den: i64 = 1
let mut i: i64 = 1
while i <= k {
num = (num * (n - (k - i))) % p
den = (den * i) % p
i = i + 1
}
return (num * modpow(den, p - 2, p)) % p
}
function s_mod_prime(n: i64, p: i64) -> i64 {
let n0: i64 = n % p
let inv2: i64 = modpow(2, p - 2, p)
let r: ptr<i64> = calloc(p, 8)
let r_exp: ptr<i64> = calloc(p, 8)
let fact: ptr<i64> = calloc(n0 + 1, 8)
let mut inv2_pow: i64 = 1
let mut prev: i64 = 1
let mut i: i64 = 1
while i < p {
inv2_pow = (inv2_pow * inv2) % p
r[i] = (inv2_pow - prev + p) % p
prev = inv2_pow
i = i + 1
}
let mut e: i64 = 0
while e < p - 1 {
let mut s: i64 = 0
i = 1
while i < p {
s = (s + r[i] * modpow(i, e, p)) % p
i = i + 1
}
r_exp[e] = s
e = e + 1
}
fact[0] = 1
i = 1
while i <= n0 {
fact[i] = (fact[i - 1] * i) % p
i = i + 1
}
let mut res: i64 = 0
let mut m: i64 = 0
while m <= n0 {
let c_nm: i64 = comb_small(n0, m, p)
let ee: i64 = (n - m) % (p - 1)
res = (res + fact[m] * c_nm % p * r_exp[ee]) % p
m = m + 1
}
free(r); free(r_exp); free(fact)
return res
}
function main() -> i32 {
let n: i64 = 1000000000
let residues: ptr<i64> = calloc(5, 8)
let mods: ptr<i64> = calloc(5, 8)
mods[0] = 7; mods[1] = 11; mods[2] = 73; mods[3] = 101; mods[4] = 137
let mut i: i64 = 0
while i < 5 {
residues[i] = s_mod_prime(n, mods[i])
i = i + 1
}
let mut x: i64 = 0
let mut m: i64 = 1
i = 0
while i < 5 {
let mi: i64 = mods[i]
let ai: i64 = residues[i]
let t: i64 = ((ai - x) % mi + mi) % mi * modpow(m % mi, mi - 2, mi) % mi
x = x + m * t
m = m * mi
i = i + 1
}
printf("%lld\n", x % m)
free(residues); free(mods)
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 base, int64_t exp, int64_t mod);
int64_t comb_small_i64_i64_i64(int64_t n, int64_t k0, int64_t p);
int64_t s_mod_prime_i64_i64(int64_t n, int64_t p);
int32_t main(void);
int64_t modpow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod) {
int64_t r = 1;
int64_t b = FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD((base), (mod)) + mod)), (mod));
int64_t e = exp;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
r = FLOW_CHECKED_MOD(((r * b)), (mod));
}
b = FLOW_CHECKED_MOD(((b * b)), (mod));
e = FLOW_CHECKED_DIV((e), (2));
}
return r;
}
int64_t comb_small_i64_i64_i64(int64_t n, int64_t k0, int64_t p) {
if ((k0 < 0 || k0 > n)) {
return 0;
}
if ((k0 == 0 || k0 == n)) {
return 1;
}
int64_t k = k0;
if (k > (n - k)) {
k = (n - k);
}
int64_t num = 1;
int64_t den = 1;
int64_t i = 1;
while (i <= k) {
num = FLOW_CHECKED_MOD(((num * (n - (k - i)))), (p));
den = FLOW_CHECKED_MOD(((den * i)), (p));
i = (i + 1);
}
return FLOW_CHECKED_MOD(((num * modpow_i64_i64_i64(den, (p - 2), p))), (p));
}
int64_t s_mod_prime_i64_i64(int64_t n, int64_t p) {
int64_t n0 = FLOW_CHECKED_MOD((n), (p));
int64_t inv2 = modpow_i64_i64_i64(2, (p - 2), p);
int64_t* r = (int64_t*)(calloc(p, 8));
int64_t* r_exp = (int64_t*)(calloc(p, 8));
int64_t* fact = (int64_t*)(calloc((n0 + 1), 8));
int64_t inv2_pow = 1;
int64_t prev = 1;
int64_t i = 1;
while (i < p) {
inv2_pow = FLOW_CHECKED_MOD(((inv2_pow * inv2)), (p));
r[i] = FLOW_CHECKED_MOD((((inv2_pow - prev) + p)), (p));
prev = inv2_pow;
i = (i + 1);
}
int64_t e = 0;
while (e < (p - 1)) {
int64_t s = 0;
i = 1;
while (i < p) {
s = FLOW_CHECKED_MOD(((s + (r[i] * modpow_i64_i64_i64(i, e, p)))), (p));
i = (i + 1);
}
r_exp[e] = s;
e = (e + 1);
}
fact[0] = 1;
i = 1;
while (i <= n0) {
fact[i] = FLOW_CHECKED_MOD(((fact[(i - 1)] * i)), (p));
i = (i + 1);
}
int64_t res = 0;
int64_t m = 0;
while (m <= n0) {
int64_t c_nm = comb_small_i64_i64_i64(n0, m, p);
int64_t ee = FLOW_CHECKED_MOD(((n - m)), ((p - 1)));
res = FLOW_CHECKED_MOD(((res + (FLOW_CHECKED_MOD(((fact[m] * c_nm)), (p)) * r_exp[ee]))), (p));
m = (m + 1);
}
free(r);
free(r_exp);
free(fact);
return res;
}
int32_t main(void) {
int64_t n = 1000000000;
int64_t* residues = (int64_t*)(calloc(5, 8));
int64_t* mods = (int64_t*)(calloc(5, 8));
mods[0] = 7;
mods[1] = 11;
mods[2] = 73;
mods[3] = 101;
mods[4] = 137;
int64_t i = 0;
while (i < 5) {
residues[i] = s_mod_prime_i64_i64(n, mods[i]);
i = (i + 1);
}
int64_t x = 0;
int64_t m = 1;
i = 0;
while (i < 5) {
int64_t mi = mods[i];
int64_t ai = residues[i];
int64_t t = FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD(((ai - x)), (mi)) + mi)), (mi)) * modpow_i64_i64_i64(FLOW_CHECKED_MOD((m), (mi)), (mi - 2), mi))), (mi));
x = (x + (m * t));
m = (m * mi);
i = (i + 1);
}
printf("%lld\n", FLOW_CHECKED_MOD((x), (m)));
free(residues);
free(mods);
return 0;
}