# Project Euler 282
# Sum A(n,n) for n=0..6 mod 14^8.
import euler.nt { gcd }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function local_mod_pow(base0: i64, exp0: i64, mod: i64) -> i64 {
if mod == 1 { return 0 }
let mut result: i64 = 1
let mut base: i64 = base0 % mod
let mut exp: i64 = exp0
while exp > 0 {
if exp % 2 == 1 { result = (result * base) % mod }
base = (base * base) % mod
exp = exp / 2
}
return result
}
function local_mulmod(a0: i64, b0: i64, mod: i64) -> i64 {
let mut a: i64 = a0 % mod
let mut b: i64 = b0 % mod
if a < 0 { a = a + mod }
if b < 0 { b = b + mod }
let mut result: i64 = 0
while b > 0 {
if b % 2 == 1 {
result = result + a
if result >= mod { result = result - mod }
}
a = a + a
if a >= mod { a = a - mod }
b = b / 2
}
return result
}
function mod_inverse(a0: i64, m: i64) -> i64 {
let mut a: i64 = a0 % m
let mut b: i64 = m
let mut x0: i64 = 1
let mut x1: i64 = 0
while b != 0 {
let q: i64 = a / b
let t: i64 = a % b
a = b
b = t
let tx: i64 = x0 - q * x1
x0 = x1
x1 = tx
}
if x0 < 0 { x0 = x0 + m }
return x0
}
function carmichael(n0: i64) -> i64 {
if n0 == 1 { return 1 }
let mut n: i64 = n0
let mut lam: i64 = 1
let mut p: i64 = 2
while p * p <= n {
if n % p == 0 {
let mut k: i64 = 0
let mut pk: i64 = 1
while n % p == 0 {
n = n / p
k = k + 1
pk = pk * p
}
let mut pk_lam: i64 = 0
if p == 2 {
if k == 1 { pk_lam = 1 }
elif k == 2 { pk_lam = 2 }
else {
let mut t: i64 = 1
let mut i: i64 = 0
while i < k - 2 {
t = t * 2
i = i + 1
}
pk_lam = t
}
} else {
pk_lam = (p - 1) * (pk / p)
}
# lcm
lam = lam / gcd(lam, pk_lam) * pk_lam
}
if p == 2 { p = 3 } else { p = p + 2 }
}
if n > 1 {
let pk_lam2: i64 = n - 1
lam = lam / gcd(lam, pk_lam2) * pk_lam2
}
return lam
}
function crt_pair(a1: i64, m1: i64, a2: i64, m2: i64) -> i64 {
let inv: i64 = mod_inverse(m1 % m2, m2)
let k: i64 = local_mulmod(((a2 - a1) % m2 + m2) % m2, inv, m2)
return (a1 + local_mulmod(k, m1, m1 * m2)) % (m1 * m2)
}
function tower_geq(h: i64, limit: i64) -> bool {
if limit <= 1 { return true }
let mut v: i64 = 2
if h == 1 { return v >= limit }
let mut i: i64 = 2
while i <= h {
if v >= 60 { return true }
# 2^v
if v >= 63 { return true }
let one: i64 = 1
v = one << v
if v >= limit { return true }
i = i + 1
}
return v >= limit
}
function tetration_exact(h: i64) -> i64 {
let mut v: i64 = 2
let mut i: i64 = 2
while i <= h {
let one: i64 = 1
v = one << v
i = i + 1
}
return v
}
# Memo for tetration_mod: height up to 60, few mods — use recursive without cache (small depth)
function tetration_mod(height: i64, mod: i64) -> i64 {
if mod == 1 { return 0 }
if height == 1 { return 2 % mod }
let mut m: i64 = mod
let mut k: i64 = 0
while m % 2 == 0 {
k = k + 1
m = m / 2
}
let mut r2: i64 = 0
if k > 0 {
let one: i64 = 1
let mod2: i64 = one << k
if tower_geq(height - 1, k) {
r2 = 0
} else {
let exp: i64 = tetration_exact(height - 1)
if exp >= k { r2 = 0 }
else { r2 = (one << exp) % mod2 }
}
if m == 1 { return r2 }
}
let lam: i64 = carmichael(m)
let exp2: i64 = tetration_mod(height - 1, lam)
let rodd: i64 = local_mod_pow(2, exp2, m)
if k == 0 { return rodd }
let one2: i64 = 1
return crt_pair(r2, one2 << k, rodd, m)
}
function main() -> i32 {
let mut mod: i64 = 1
let mut i: i64 = 0
while i < 8 {
mod = mod * 14
i = i + 1
}
let a0: i64 = 1 % mod
let a1: i64 = 3 % mod
let a2: i64 = 7 % mod
let a3: i64 = 61 % mod
let a4: i64 = (tetration_mod(7, mod) - 3) % mod
if a4 < 0 { a4 = a4 + mod }
# find fixed point of tetration
let mut prev: i64 = tetration_mod(1, mod)
let mut fixed_h: i64 = 1
let mut h: i64 = 2
while h <= 60 {
let cur: i64 = tetration_mod(h, mod)
if cur == prev {
fixed_h = h - 1
break
}
prev = cur
h = h + 1
}
let fixed_val: i64 = (tetration_mod(fixed_h, mod) - 3) % mod
if fixed_val < 0 { fixed_val = fixed_val + mod }
let a5: i64 = fixed_val
let a6: i64 = fixed_val
let ans: i64 = (a0 + a1 + a2 + a3 + a4 + a5 + a6) % 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 gcd_i64_i64(int64_t a0, int64_t b0);
int64_t lcm_i64_i64(int64_t a, int64_t b);
int64_t isqrt_i64(int64_t n);
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod);
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod);
bool is_prime_i64(int64_t n);
int64_t local_mod_pow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod);
int64_t local_mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod);
int64_t mod_inverse_i64_i64(int64_t a0, int64_t m);
int64_t carmichael_i64(int64_t n0);
int64_t crt_pair_i64_i64_i64_i64(int64_t a1, int64_t m1, int64_t a2, int64_t m2);
bool tower_geq_i64_i64(int64_t h, int64_t limit);
int64_t tetration_exact_i64(int64_t h);
int64_t tetration_mod_i64_i64(int64_t height, int64_t mod);
int32_t main(void);
int64_t gcd_i64_i64(int64_t a0, int64_t b0) {
int64_t a = a0;
int64_t b = b0;
while (b != 0) {
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
}
return a;
}
int64_t lcm_i64_i64(int64_t a, int64_t b) {
if ((a == 0 || b == 0)) {
return 0;
}
return (FLOW_CHECKED_DIV((a), (gcd_i64_i64(a, b))) * b);
}
int64_t isqrt_i64(int64_t n) {
if (n < 2) {
return n;
}
int64_t x = n;
int64_t y = FLOW_CHECKED_DIV(((x + 1)), (2));
while (y < x) {
x = y;
y = FLOW_CHECKED_DIV(((x + FLOW_CHECKED_DIV((n), (x)))), (2));
}
return x;
}
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod) {
int64_t a = FLOW_CHECKED_MOD((a0), (mod));
int64_t b = FLOW_CHECKED_MOD((b0), (mod));
int64_t result = 0;
while (b > 0) {
if (FLOW_CHECKED_MOD((b), (2)) == 1) {
result = FLOW_CHECKED_MOD(((result + a)), (mod));
}
a = FLOW_CHECKED_MOD(((a * 2)), (mod));
b = FLOW_CHECKED_DIV((b), (2));
}
return result;
}
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod) {
if (mod == 1) {
return 0;
}
int64_t result = 1;
int64_t b = FLOW_CHECKED_MOD((base), (mod));
int64_t e = exp;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
result = mulmod_i64_i64_i64(result, b, mod);
}
b = mulmod_i64_i64_i64(b, b, mod);
e = FLOW_CHECKED_DIV((e), (2));
}
return result;
}
bool is_prime_i64(int64_t n) {
if (n < 2) {
return 0;
}
if (n < 4) {
return 1;
}
if ((FLOW_CHECKED_MOD((n), (2)) == 0 || FLOW_CHECKED_MOD((n), (3)) == 0)) {
return 0;
}
int64_t i = 5;
while ((i * i) <= n) {
if ((FLOW_CHECKED_MOD((n), (i)) == 0 || FLOW_CHECKED_MOD((n), ((i + 2))) == 0)) {
return 0;
}
i = (i + 6);
}
return 1;
}
int64_t local_mod_pow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod) {
if (mod == 1) {
return 0;
}
int64_t result = 1;
int64_t base = FLOW_CHECKED_MOD((base0), (mod));
int64_t exp = exp0;
while (exp > 0) {
if (FLOW_CHECKED_MOD((exp), (2)) == 1) {
result = FLOW_CHECKED_MOD(((result * base)), (mod));
}
base = FLOW_CHECKED_MOD(((base * base)), (mod));
exp = FLOW_CHECKED_DIV((exp), (2));
}
return result;
}
int64_t local_mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod) {
int64_t a = FLOW_CHECKED_MOD((a0), (mod));
int64_t b = FLOW_CHECKED_MOD((b0), (mod));
if (a < 0) {
a = (a + mod);
}
if (b < 0) {
b = (b + mod);
}
int64_t result = 0;
while (b > 0) {
if (FLOW_CHECKED_MOD((b), (2)) == 1) {
result = (result + a);
if (result >= mod) {
result = (result - mod);
}
}
a = (a + a);
if (a >= mod) {
a = (a - mod);
}
b = FLOW_CHECKED_DIV((b), (2));
}
return result;
}
int64_t mod_inverse_i64_i64(int64_t a0, int64_t m) {
int64_t a = FLOW_CHECKED_MOD((a0), (m));
int64_t b = m;
int64_t x0 = 1;
int64_t x1 = 0;
while (b != 0) {
int64_t q = FLOW_CHECKED_DIV((a), (b));
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
int64_t tx = (x0 - (q * x1));
x0 = x1;
x1 = tx;
}
if (x0 < 0) {
x0 = (x0 + m);
}
return x0;
}
int64_t carmichael_i64(int64_t n0) {
if (n0 == 1) {
return 1;
}
int64_t n = n0;
int64_t lam = 1;
int64_t p = 2;
while ((p * p) <= n) {
if (FLOW_CHECKED_MOD((n), (p)) == 0) {
int64_t k = 0;
int64_t pk = 1;
while (FLOW_CHECKED_MOD((n), (p)) == 0) {
n = FLOW_CHECKED_DIV((n), (p));
k = (k + 1);
pk = (pk * p);
}
int64_t pk_lam = 0;
if (p == 2) {
if (k == 1) {
pk_lam = 1;
} else if (k == 2) {
pk_lam = 2;
} else {
int64_t t = 1;
int64_t i = 0;
while (i < (k - 2)) {
t = (t * 2);
i = (i + 1);
}
pk_lam = t;
}
} else {
pk_lam = ((p - 1) * FLOW_CHECKED_DIV((pk), (p)));
}
lam = (FLOW_CHECKED_DIV((lam), (gcd_i64_i64(lam, pk_lam))) * pk_lam);
}
if (p == 2) {
p = 3;
} else {
p = (p + 2);
}
}
if (n > 1) {
int64_t pk_lam2 = (n - 1);
lam = (FLOW_CHECKED_DIV((lam), (gcd_i64_i64(lam, pk_lam2))) * pk_lam2);
}
return lam;
}
int64_t crt_pair_i64_i64_i64_i64(int64_t a1, int64_t m1, int64_t a2, int64_t m2) {
int64_t inv = mod_inverse_i64_i64(FLOW_CHECKED_MOD((m1), (m2)), m2);
int64_t k = local_mulmod_i64_i64_i64(FLOW_CHECKED_MOD(((FLOW_CHECKED_MOD(((a2 - a1)), (m2)) + m2)), (m2)), inv, m2);
return FLOW_CHECKED_MOD(((a1 + local_mulmod_i64_i64_i64(k, m1, (m1 * m2)))), ((m1 * m2)));
}
bool tower_geq_i64_i64(int64_t h, int64_t limit) {
if (limit <= 1) {
return 1;
}
int64_t v = 2;
if (h == 1) {
return v >= limit;
}
int64_t i = 2;
while (i <= h) {
if (v >= 60) {
return 1;
}
if (v >= 63) {
return 1;
}
int64_t one = 1;
v = FLOW_CHECKED_SHL((one), (v));
if (v >= limit) {
return 1;
}
i = (i + 1);
}
return v >= limit;
}
int64_t tetration_exact_i64(int64_t h) {
int64_t v = 2;
int64_t i = 2;
while (i <= h) {
int64_t one = 1;
v = FLOW_CHECKED_SHL((one), (v));
i = (i + 1);
}
return v;
}
int64_t tetration_mod_i64_i64(int64_t height, int64_t mod) {
if (mod == 1) {
return 0;
}
if (height == 1) {
return FLOW_CHECKED_MOD((2), (mod));
}
int64_t m = mod;
int64_t k = 0;
while (FLOW_CHECKED_MOD((m), (2)) == 0) {
k = (k + 1);
m = FLOW_CHECKED_DIV((m), (2));
}
int64_t r2 = 0;
if (k > 0) {
int64_t one = 1;
int64_t mod2 = FLOW_CHECKED_SHL((one), (k));
if (tower_geq_i64_i64((height - 1), k)) {
r2 = 0;
} else {
int64_t exp = tetration_exact_i64((height - 1));
if (exp >= k) {
r2 = 0;
} else {
r2 = FLOW_CHECKED_MOD((FLOW_CHECKED_SHL((one), (exp))), (mod2));
}
}
if (m == 1) {
return r2;
}
}
int64_t lam = carmichael_i64(m);
int64_t exp2 = tetration_mod_i64_i64((height - 1), lam);
int64_t rodd = local_mod_pow_i64_i64_i64(2, exp2, m);
if (k == 0) {
return rodd;
}
int64_t one2 = 1;
return crt_pair_i64_i64_i64_i64(r2, FLOW_CHECKED_SHL((one2), (k)), rodd, m);
}
int32_t main(void) {
int64_t mod = 1;
int64_t i = 0;
while (i < 8) {
mod = (mod * 14);
i = (i + 1);
}
int64_t a0 = FLOW_CHECKED_MOD((1), (mod));
int64_t a1 = FLOW_CHECKED_MOD((3), (mod));
int64_t a2 = FLOW_CHECKED_MOD((7), (mod));
int64_t a3 = FLOW_CHECKED_MOD((61), (mod));
int64_t a4 = FLOW_CHECKED_MOD(((tetration_mod_i64_i64(7, mod) - 3)), (mod));
if (a4 < 0) {
a4 = (a4 + mod);
}
int64_t prev = tetration_mod_i64_i64(1, mod);
int64_t fixed_h = 1;
int64_t h = 2;
while (h <= 60) {
int64_t cur = tetration_mod_i64_i64(h, mod);
if (cur == prev) {
fixed_h = (h - 1);
break;
}
prev = cur;
h = (h + 1);
}
int64_t fixed_val = FLOW_CHECKED_MOD(((tetration_mod_i64_i64(fixed_h, mod) - 3)), (mod));
if (fixed_val < 0) {
fixed_val = (fixed_val + mod);
}
int64_t a5 = fixed_val;
int64_t a6 = fixed_val;
int64_t ans = FLOW_CHECKED_MOD((((((((a0 + a1) + a2) + a3) + a4) + a5) + a6)), (mod));
printf("%lld\n", ans);
return 0;
}