# Project Euler 475
# Music Festival — f(600) mod 1_000_000_007.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
let mut MOD: i64 = 1000000007
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
if b < 0 { b = b + mod }
while e > 0 {
if e % 2 == 1 {
r = (r * b) % mod
}
b = (b * b) % mod
e = e / 2
}
return r
}
function main() -> i32 {
# f(12n) with n = 50 => f(600)
let n: i64 = 50
let E: i64 = 4 * n
let m: i64 = 3 * n
let limit: i64 = 16 * n + 10
let fact: ptr<i64> = calloc(limit + 1, 8)
let invfact: ptr<i64> = calloc(limit + 1, 8)
let pow2: ptr<i64> = calloc(E + 1, 8)
let pow_neg3: ptr<i64> = calloc(E + 1, 8)
let inv24pow: ptr<i64> = calloc(m + 1, 8)
let inv2pow: ptr<i64> = calloc(E + 1, 8)
if fact == null || invfact == null || pow2 == null || pow_neg3 == null || inv24pow == null || inv2pow == null {
return 1
}
fact[0] = 1
let mut i: i64 = 1
while i <= limit {
fact[i] = (fact[i - 1] * i) % MOD
i = i + 1
}
invfact[limit] = modpow(fact[limit], MOD - 2, MOD)
i = limit
while i > 0 {
invfact[i - 1] = (invfact[i] * i) % MOD
i = i - 1
}
pow2[0] = 1
i = 1
while i <= E {
pow2[i] = (pow2[i - 1] * 2) % MOD
i = i + 1
}
let neg3: i64 = MOD - 3
pow_neg3[0] = 1
i = 1
while i <= E {
pow_neg3[i] = (pow_neg3[i - 1] * neg3) % MOD
i = i + 1
}
let inv2: i64 = (MOD + 1) / 2
let inv24: i64 = modpow(24, MOD - 2, MOD)
inv24pow[0] = 1
i = 1
while i <= m {
inv24pow[i] = (inv24pow[i - 1] * inv24) % MOD
i = i + 1
}
inv2pow[0] = 1
i = 1
while i <= E {
inv2pow[i] = (inv2pow[i - 1] * inv2) % MOD
i = i + 1
}
let mut sigma: i64 = 0
i = 0
while i <= E {
let max_j: i64 = E - i
let mut j: i64 = 0
while j <= max_j {
let k: i64 = E - i - j
let A: i64 = 3 * i + j
let mut base: i64 = (fact[A] * invfact[i]) % MOD
base = (base * pow_neg3[j]) % MOD
base = (base * pow2[k]) % MOD
let mut dmin: i64 = 0
if i < n {
dmin = n - i
}
let dmax: i64 = j / 2
if dmin <= dmax {
let invfact_c: i64 = invfact[k]
let mut sumd: i64 = 0
let mut d: i64 = dmin
while d <= dmax {
let a: i64 = i - n + d
let b: i64 = j - 2 * d
let mut term: i64 = invfact[a]
term = (term * invfact[b]) % MOD
term = (term * invfact_c) % MOD
term = (term * invfact[d]) % MOD
term = (term * inv24pow[a]) % MOD
term = (term * inv2pow[b + d]) % MOD
sumd = (sumd + term) % MOD
d = d + 1
}
sigma = (sigma + base * sumd) % MOD
}
j = j + 1
}
i = i + 1
}
let pow24m: i64 = modpow(24, m, MOD)
let inv6E: i64 = modpow(modpow(6, E, MOD), MOD - 2, MOD)
let mut ans: i64 = (pow24m * fact[m]) % MOD
ans = (ans * sigma) % MOD
ans = (ans * inv6E) % MOD
printf("%lld\n", ans)
free(fact)
free(invfact)
free(pow2)
free(pow_neg3)
free(inv24pow)
free(inv2pow)
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);
int32_t main(void);
/* Module statics */
static int64_t MOD = 1000000007;
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;
if (b < 0) {
b = (b + mod);
}
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;
}
int32_t main(void) {
int64_t n = 50;
int64_t E = (4 * n);
int64_t m = (3 * n);
int64_t limit = ((16 * n) + 10);
int64_t* fact = (int64_t*)(calloc((limit + 1), 8));
int64_t* invfact = (int64_t*)(calloc((limit + 1), 8));
int64_t* pow2 = (int64_t*)(calloc((E + 1), 8));
int64_t* pow_neg3 = (int64_t*)(calloc((E + 1), 8));
int64_t* inv24pow = (int64_t*)(calloc((m + 1), 8));
int64_t* inv2pow = (int64_t*)(calloc((E + 1), 8));
if ((((((fact == NULL || invfact == NULL) || pow2 == NULL) || pow_neg3 == NULL) || inv24pow == NULL) || inv2pow == NULL)) {
return 1;
}
fact[0] = 1;
int64_t i = 1;
while (i <= limit) {
fact[i] = FLOW_CHECKED_MOD(((fact[(i - 1)] * i)), (MOD));
i = (i + 1);
}
invfact[limit] = modpow_i64_i64_i64(fact[limit], (MOD - 2), MOD);
i = limit;
while (i > 0) {
invfact[(i - 1)] = FLOW_CHECKED_MOD(((invfact[i] * i)), (MOD));
i = (i - 1);
}
pow2[0] = 1;
i = 1;
while (i <= E) {
pow2[i] = FLOW_CHECKED_MOD(((pow2[(i - 1)] * 2)), (MOD));
i = (i + 1);
}
int64_t neg3 = (MOD - 3);
pow_neg3[0] = 1;
i = 1;
while (i <= E) {
pow_neg3[i] = FLOW_CHECKED_MOD(((pow_neg3[(i - 1)] * neg3)), (MOD));
i = (i + 1);
}
int64_t inv2 = FLOW_CHECKED_DIV(((MOD + 1)), (2));
int64_t inv24 = modpow_i64_i64_i64(24, (MOD - 2), MOD);
inv24pow[0] = 1;
i = 1;
while (i <= m) {
inv24pow[i] = FLOW_CHECKED_MOD(((inv24pow[(i - 1)] * inv24)), (MOD));
i = (i + 1);
}
inv2pow[0] = 1;
i = 1;
while (i <= E) {
inv2pow[i] = FLOW_CHECKED_MOD(((inv2pow[(i - 1)] * inv2)), (MOD));
i = (i + 1);
}
int64_t sigma = 0;
i = 0;
while (i <= E) {
int64_t max_j = (E - i);
int64_t j = 0;
while (j <= max_j) {
int64_t k = ((E - i) - j);
int64_t A = ((3 * i) + j);
int64_t base = FLOW_CHECKED_MOD(((fact[A] * invfact[i])), (MOD));
base = FLOW_CHECKED_MOD(((base * pow_neg3[j])), (MOD));
base = FLOW_CHECKED_MOD(((base * pow2[k])), (MOD));
int64_t dmin = 0;
if (i < n) {
dmin = (n - i);
}
int64_t dmax = FLOW_CHECKED_DIV((j), (2));
if (dmin <= dmax) {
int64_t invfact_c = invfact[k];
int64_t sumd = 0;
int64_t d = dmin;
while (d <= dmax) {
int64_t a = ((i - n) + d);
int64_t b = (j - (2 * d));
int64_t term = invfact[a];
term = FLOW_CHECKED_MOD(((term * invfact[b])), (MOD));
term = FLOW_CHECKED_MOD(((term * invfact_c)), (MOD));
term = FLOW_CHECKED_MOD(((term * invfact[d])), (MOD));
term = FLOW_CHECKED_MOD(((term * inv24pow[a])), (MOD));
term = FLOW_CHECKED_MOD(((term * inv2pow[(b + d)])), (MOD));
sumd = FLOW_CHECKED_MOD(((sumd + term)), (MOD));
d = (d + 1);
}
sigma = FLOW_CHECKED_MOD(((sigma + (base * sumd))), (MOD));
}
j = (j + 1);
}
i = (i + 1);
}
int64_t pow24m = modpow_i64_i64_i64(24, m, MOD);
int64_t inv6E = modpow_i64_i64_i64(modpow_i64_i64_i64(6, E, MOD), (MOD - 2), MOD);
int64_t ans = FLOW_CHECKED_MOD(((pow24m * fact[m])), (MOD));
ans = FLOW_CHECKED_MOD(((ans * sigma)), (MOD));
ans = FLOW_CHECKED_MOD(((ans * inv6E)), (MOD));
printf("%lld\n", ans);
free(fact);
free(invfact);
free(pow2);
free(pow_neg3);
free(inv24pow);
free(inv2pow);
return 0;
}