# Project Euler 409
# W(10^7) mod 10^9+7: winning nim positions with distinct pile sizes.
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 main() -> i32 {
let N: i64 = 10000000
let MOD: i64 = 1000000007
let q: i64 = modpow(2, N, MOD)
let q_minus_1: i64 = q - 1
if q_minus_1 < 0 { q_minus_1 = q_minus_1 + MOD }
let mut total: i64 = 1
let mut fact: i64 = 1
let mut term: i64 = q_minus_1
let mut i: i64 = 1
while i <= N {
let t: i128 = (total as i128) * (term as i128) % (MOD as i128)
total = t as i64
term = term - 1
if term < 0 { term = term + MOD }
let t2: i128 = (fact as i128) * (i as i128) % (MOD as i128)
fact = t2 as i64
i = i + 1
}
let inv_fact: i64 = modpow(fact, MOD - 2, MOD)
let comb: i64 = ((total as i128) * (inv_fact as i128) % (MOD as i128)) as i64
let m: i64 = N / 2
let mut s: i64 = 1
if m > 0 {
let inv: ptr<i64> = calloc(m + 1, 8)
if inv == null { return 1 }
inv[1] = 1
i = 2
while i <= m {
inv[i] = MOD - ((MOD / i) * inv[MOD % i]) % MOD
i = i + 1
}
let n_half: i64 = modpow(2, N - 1, MOD)
let mut binom: i64 = 1
let mut r: i64 = 1
while r <= m {
let tr: i64 = (n_half - r + 1) % MOD
if tr < 0 { tr = tr + MOD }
binom = ((binom as i128) * (tr as i128) % (MOD as i128)) as i64
binom = ((binom as i128) * (inv[r] as i128) % (MOD as i128)) as i64
if r % 2 == 1 {
s = s - binom
} else {
s = s + binom
}
s = s % MOD
if s < 0 { s = s + MOD }
r = r + 1
}
free(inv)
}
let mut e_n: i64 = s
if N % 2 == 1 {
e_n = (0 - s) % MOD
if e_n < 0 { e_n = e_n + MOD }
}
let inv_q: i64 = modpow(q, MOD - 2, MOD)
let mut losing: i64 = ((fact as i128) * (inv_q as i128) % (MOD as i128)) as i64
let inner: i64 = (comb + ((q_minus_1 as i128) * (e_n as i128) % (MOD as i128)) as i64) % MOD
losing = ((losing as i128) * (inner as i128) % (MOD as i128)) as i64
let ans: i64 = (total - losing) % MOD
if ans < 0 { ans = ans + MOD }
printf("%lld\n", ans)
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);
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;
}
int32_t main(void) {
int64_t N = 10000000;
int64_t MOD = 1000000007;
int64_t q = modpow_i64_i64_i64(2, N, MOD);
int64_t q_minus_1 = (q - 1);
if (q_minus_1 < 0) {
q_minus_1 = (q_minus_1 + MOD);
}
int64_t total = 1;
int64_t fact = 1;
int64_t term = q_minus_1;
int64_t i = 1;
while (i <= N) {
__int128 t = FLOW_CHECKED_MOD(((((__int128)(total)) * ((__int128)(term)))), (((__int128)(MOD))));
total = ((int64_t)(t));
term = (term - 1);
if (term < 0) {
term = (term + MOD);
}
__int128 t2 = FLOW_CHECKED_MOD(((((__int128)(fact)) * ((__int128)(i)))), (((__int128)(MOD))));
fact = ((int64_t)(t2));
i = (i + 1);
}
int64_t inv_fact = modpow_i64_i64_i64(fact, (MOD - 2), MOD);
int64_t comb = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(total)) * ((__int128)(inv_fact)))), (((__int128)(MOD))))));
int64_t m = FLOW_CHECKED_DIV((N), (2));
int64_t s = 1;
if (m > 0) {
int64_t* inv = (int64_t*)(calloc((m + 1), 8));
if (inv == NULL) {
return 1;
}
inv[1] = 1;
i = 2;
while (i <= m) {
inv[i] = (MOD - FLOW_CHECKED_MOD(((FLOW_CHECKED_DIV((MOD), (i)) * inv[FLOW_CHECKED_MOD((MOD), (i))])), (MOD)));
i = (i + 1);
}
int64_t n_half = modpow_i64_i64_i64(2, (N - 1), MOD);
int64_t binom = 1;
int64_t r = 1;
while (r <= m) {
int64_t tr = FLOW_CHECKED_MOD((((n_half - r) + 1)), (MOD));
if (tr < 0) {
tr = (tr + MOD);
}
binom = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(binom)) * ((__int128)(tr)))), (((__int128)(MOD))))));
binom = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(binom)) * ((__int128)(inv[r])))), (((__int128)(MOD))))));
if (FLOW_CHECKED_MOD((r), (2)) == 1) {
s = (s - binom);
} else {
s = (s + binom);
}
s = FLOW_CHECKED_MOD((s), (MOD));
if (s < 0) {
s = (s + MOD);
}
r = (r + 1);
}
free(inv);
}
int64_t e_n = s;
if (FLOW_CHECKED_MOD((N), (2)) == 1) {
e_n = FLOW_CHECKED_MOD(((0 - s)), (MOD));
if (e_n < 0) {
e_n = (e_n + MOD);
}
}
int64_t inv_q = modpow_i64_i64_i64(q, (MOD - 2), MOD);
int64_t losing = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(fact)) * ((__int128)(inv_q)))), (((__int128)(MOD))))));
int64_t inner = FLOW_CHECKED_MOD(((comb + ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(q_minus_1)) * ((__int128)(e_n)))), (((__int128)(MOD)))))))), (MOD));
losing = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(losing)) * ((__int128)(inner)))), (((__int128)(MOD))))));
int64_t ans = FLOW_CHECKED_MOD(((total - losing)), (MOD));
if (ans < 0) {
ans = (ans + MOD);
}
printf("%lld\n", ans);
return 0;
}