# Project Euler 822
# Square the Smallest — S(10^4, 10^16) mod 1234567891.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
const MOD: i64 = 1234567891
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 & 1) != 0 {
r = ((r as i128) * (b as i128) % (mod as i128)) as i64
}
b = ((b as i128) * (b as i128) % (mod as i128)) as i64
e = e >> 1
}
return r
}
function S(n: i64, m: i64) -> i64 {
let A: ptr<i64> = calloc(n - 1, 8)
let mut i: i64 = 0
while i < n - 1 {
A[i] = i + 2
i = i + 1
}
let mut k: i64 = 0
while 1 == 1 {
let mut mn: i64 = A[0]
let mut mx: i64 = A[0]
let mut mi: i64 = 0
i = 1
while i < n - 1 {
if A[i] < mn {
mn = A[i]
mi = i
}
if A[i] > mx { mx = A[i] }
i = i + 1
}
if mn * mn >= mx { break }
A[mi] = mn * mn
k = k + 1
}
# sort A
i = 0
while i < n - 1 {
let mut j: i64 = i + 1
while j < n - 1 {
if A[j] < A[i] {
let t: i64 = A[i]
A[i] = A[j]
A[j] = t
}
j = j + 1
}
i = i + 1
}
let q: i64 = (m - k) / (n - 1)
let r: i64 = (m - k) % (n - 1)
let mut total: i64 = 0
i = 0
while i < n - 1 {
let mut exp2: i64 = q
if i < r { exp2 = q + 1 }
# A[i]^(2^exp2) mod MOD using phi(MOD)=MOD-1
let e: i64 = modpow(2, exp2, MOD - 1)
total = (total + modpow(A[i], e, MOD)) % MOD
i = i + 1
}
free(A)
return total
}
function main() -> i32 {
printf("%lld\n", S(10000, 10000000000000000))
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 S_i64_i64(int64_t n, int64_t m);
int32_t main(void);
static const int64_t MOD = 1234567891;
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 ((e & 1) != 0) {
r = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(r)) * ((__int128)(b)))), (((__int128)(mod))))));
}
b = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(b)))), (((__int128)(mod))))));
e = FLOW_CHECKED_SHR((e), (1));
}
return r;
}
int64_t S_i64_i64(int64_t n, int64_t m) {
int64_t* A = (int64_t*)(calloc((n - 1), 8));
int64_t i = 0;
while (i < (n - 1)) {
A[i] = (i + 2);
i = (i + 1);
}
int64_t k = 0;
while (1 == 1) {
int64_t mn = A[0];
int64_t mx = A[0];
int64_t mi = 0;
i = 1;
while (i < (n - 1)) {
if (A[i] < mn) {
mn = A[i];
mi = i;
}
if (A[i] > mx) {
mx = A[i];
}
i = (i + 1);
}
if ((mn * mn) >= mx) {
break;
}
A[mi] = (mn * mn);
k = (k + 1);
}
i = 0;
while (i < (n - 1)) {
int64_t j = (i + 1);
while (j < (n - 1)) {
if (A[j] < A[i]) {
int64_t t = A[i];
A[i] = A[j];
A[j] = t;
}
j = (j + 1);
}
i = (i + 1);
}
int64_t q = FLOW_CHECKED_DIV(((m - k)), ((n - 1)));
int64_t r = FLOW_CHECKED_MOD(((m - k)), ((n - 1)));
int64_t total = 0;
i = 0;
while (i < (n - 1)) {
int64_t exp2 = q;
if (i < r) {
exp2 = (q + 1);
}
int64_t e = modpow_i64_i64_i64(2, exp2, (MOD - 1));
total = FLOW_CHECKED_MOD(((total + modpow_i64_i64_i64(A[i], e, MOD))), (MOD));
i = (i + 1);
}
free(A);
return total;
}
int32_t main(void) {
printf("%lld\n", S_i64_i64(10000, 10000000000000000));
return 0;
}