結果
| 問題 |
No.8030 ミラー・ラビン素数判定法のテスト
|
| ユーザー |
 Jashinchan
|
| 提出日時 | 2022-10-06 17:22:41 |
| 言語 | C (gcc 13.3.0) |
| 結果 |
AC
|
| 実行時間 | 83 ms / 9,973 ms |
| コード長 | 28,733 bytes |
| コンパイル時間 | 1,737 ms |
| コンパイル使用メモリ | 63,036 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2025-01-03 09:07:15 |
| 合計ジャッジ時間 | 2,664 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 10 |
ソースコード
#pragma GCC optimize("O3")
#pragma GCC target("avx2")
#pragma GCC optimize("fast-math")
#pragma GCC optimize("unroll-loops")
#define _GNU_SOURCE
#include <assert.h>
#include <inttypes.h>
#include <limits.h>
#include <math.h>
#include <stdbool.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
typedef int8_t i8;
typedef int16_t i16;
typedef int32_t i32;
typedef int64_t i64;
typedef __int128_t i128;
typedef uint8_t u8;
typedef uint16_t u16;
typedef uint32_t u32;
typedef uint64_t u64;
typedef __uint128_t u128;
typedef float f32;
typedef double f64;
typedef long double f80;
#define PRIVATE static
#define PUBLIC
#define MIN(a, b) ((a) < (b) ? (a) : (b))
#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define SWAP(a, b) \
do { \
(a) ^= (b); \
(b) ^= (a); \
(a) ^= (b); \
} \
while (0);
#define CTZ32(a) ((a) ? __builtin_ctz((a)) : (32))
#define CTZ64(a) ((a) ? __builtin_ctzll((a)) : (64))
#define CLZ32(a) ((a) ? __builtin_clz((a)) : (32))
#define CLZ64(a) ((a) ? __builtin_clzll((a)) : (64))
#define POPCNT32(a) ((a) ? __builtin_popcount((a)) : (0))
#define POPCNT64(a) ((a) ? __builtin_popcountll((a)) : (0))
#define BIT_WIDTH32(a) ((32) - CLZ32((a)))
#define BIT_WIDTH64(a) ((64) - CLZ64((a)))
#define BIT_FLOOR32(a) ((a) ? ((1u) << (BIT_WIDTH32((a)) - (1))) : (0))
#define BIT_FLOOR64(a) ((a) ? ((1ul) << (BIT_WIDTH64((a)) - (1))) : (0))
#define BIT_CEIL32(a) (((a) <= 1) ? (1u) : ((1u) << BIT_WIDTH32((a) - (1))))
#define BIT_CEIL64(a) (((a) <= 1) ? (1ul) : ((1ul) << BIT_WIDTH64((a) - (1))))
#define LSBit(a) ((a) & (-(a)))
#define CLSBit(a) ((a) & ((a) - (1)))
#define HAS_SINGLE_BIT32(a) (((a) != (0)) && (CLSBit((a)) == (0)))
#define HAS_SINGLE_BIT64(a) (((a) != (0)) && (CLSBit((a)) == (0)))
#define _ROTL32_INNER(x, l) (((x) << (l)) | ((x) >> ((-l) & (31))))
#define _ROTR32_INNER(x, r) (((x) >> (r)) | ((x) << ((-r) & (31))))
#define _ROTL64_INNER(x, l) (((x) << (l)) | ((x) >> ((-l) & (63))))
#define _ROTR64_INNER(x, r) (((x) >> (r)) | ((x) << ((-r) & (63))))
#define ROTR32(x, r) (((r) < (0)) ? (_ROTL32_INNER((x), ((u64)(-r) % (32)))) : (_ROTR32_INNER((x), ((r) % (32)))))
#define ROTL32(x, l) ROTR32((x), (-l))
#define ROTR64(x, r) (((r) < (0)) ? (_ROTL64_INNER((x), ((u64)(-r) % (64)))) : (_ROTR64_INNER((x), ((r) % (64)))))
#define ROTL64(x, l) ROTR64((x), (-l))
i32 in_i32(void)
{
i32 c, x = 0, f = 1;
while (c = getchar_unlocked(), c < 48 || c > 57)
if (c == 45)
f = -f;
while (47 < c && c < 58)
{
x = x * 10 + c - 48;
c = getchar_unlocked();
}
return f * x;
}
i64 in_i64(void)
{
i64 c, x = 0, f = 1;
while (c = getchar_unlocked(), c < 48 || c > 57)
if (c == 45)
f = -f;
while (47 < c && c < 58)
{
x = x * 10 + c - 48;
c = getchar_unlocked();
}
return f * x;
}
i128 in_i128(void)
{
i128 c, x = 0, f = 1;
while (c = getchar_unlocked(), c < 48 || c > 57)
if (c == 45)
f = -f;
while (47 < c && c < 58)
{
x = x * 10 + c - 48;
c = getchar_unlocked();
}
return f * x;
}
u32 in_u32(void)
{
u32 c, x = 0;
while (c = getchar_unlocked(), c < 48 || c > 57)
;
while (47 < c && c < 58)
{
x = x * 10 + c - 48;
c = getchar_unlocked();
}
return x;
}
u64 in_u64(void)
{
u64 c, x = 0;
while (c = getchar_unlocked(), c < 48 || c > 57)
;
while (47 < c && c < 58)
{
x = x * 10 + c - 48;
c = getchar_unlocked();
}
return x;
}
u128 in_u128(void)
{
u128 c, x = 0;
while (c = getchar_unlocked(), c < 48 || c > 57)
;
while (47 < c && c < 58)
{
x = x * 10 + c - 48;
c = getchar_unlocked();
}
return x;
}
static inline void out_i32_inner(i32 x)
{
if (x >= 10)
out_i32_inner(x / 10);
putchar_unlocked(x - x / 10 * 10 + 48);
}
void out_i32(i32 x)
{
if (x < 0)
{
putchar_unlocked('-');
x = -x;
}
out_i32_inner(x);
}
static inline void out_i64_inner(i64 x)
{
if (x >= 10)
out_i64_inner(x / 10);
putchar_unlocked(x - x / 10 * 10 + 48);
}
void out_i64(i64 x)
{
if (x < 0)
{
putchar_unlocked('-');
x = -x;
}
out_i64_inner(x);
}
static inline void out_i128_inner(i128 x)
{
if (x >= 10)
out_i128_inner(x / 10);
putchar_unlocked(x - x / 10 * 10 + 48);
}
void out_i128(i128 x)
{
if (x < 0)
{
putchar_unlocked('-');
x = -x;
}
out_i128_inner(x);
}
void out_u32(u32 x)
{
if (x >= 10)
out_u32(x / 10);
putchar_unlocked(x - x / 10 * 10 + 48);
}
void out_u64(u64 x)
{
if (x >= 10)
out_u64(x / 10);
putchar_unlocked(x - x / 10 * 10 + 48);
}
void out_u128(u128 x)
{
if (x >= 10)
out_u128(x / 10);
putchar_unlocked(x - x / 10 * 10 + 48);
}
void NL(void)
{
putchar_unlocked('\n');
}
void SP(void)
{
putchar_unlocked(' ');
}
void dump_i32(i32 x)
{
fprintf(stderr, "\033[1;36m%" PRId32 "\033[0m\n", x);
}
void dump_i64(i64 x)
{
fprintf(stderr, "\033[1;36m%" PRId64 "\033[0m\n", x);
}
void dump_u32(u32 x)
{
fprintf(stderr, "\033[1;36m%" PRIu32 "\033[0m\n", x);
}
void dump_u64(u64 x)
{
fprintf(stderr, "\033[1;36m%" PRIu64 "\033[0m\n", x);
}
void dump_i32_array(size_t a_len, i32 *a)
{
for (size_t i = 0; i < a_len; i++)
{
if (i == a_len - 1)
{
fprintf(stderr, "\033[1;36m%" PRId32 "\033[0m\n", a[i]);
}
else
{
fprintf(stderr, "\033[1;36m%" PRId32 "\033[0m ", a[i]);
}
}
}
void dump_i64_array(size_t a_len, i64 *a)
{
for (size_t i = 0; i < a_len; i++)
{
if (i == a_len - 1)
{
fprintf(stderr, "\033[1;36m%" PRId64 "\033[0m\n", a[i]);
}
else
{
fprintf(stderr, "\033[1;36m%" PRId64 "\033[0m ", a[i]);
}
}
}
void dump_u32_array(size_t a_len, u32 *a)
{
for (size_t i = 0; i < a_len; i++)
{
if (i == a_len - 1)
{
fprintf(stderr, "\033[1;36m%" PRIu32 "\033[0m\n", a[i]);
}
else
{
fprintf(stderr, "\033[1;36m%" PRIu32 "\033[0m ", a[i]);
}
}
}
void dump_u64_array(size_t a_len, u64 *a)
{
for (size_t i = 0; i < a_len; i++)
{
if (i == a_len - 1)
{
fprintf(stderr, "\033[1;36m%" PRIu64 "\033[0m\n", a[i]);
}
else
{
fprintf(stderr, "\033[1;36m%" PRIu64 "\033[0m ", a[i]);
}
}
}
void dump_i32_array_range(size_t a_len, i32 *a, size_t l, size_t r)
{
if (a_len <= r)
{
r = a_len - 1;
}
if (l > r)
{
return;
}
for (size_t i = l; i <= r; i++)
{
if (i == r)
{
fprintf(stderr, "\033[1;36m%" PRId32 "\033[0m\n", a[i]);
}
else
{
fprintf(stderr, "\033[1;36m%" PRId32 "\033[0m ", a[i]);
}
}
}
void dump_i64_array_range(size_t a_len, i64 *a, size_t l, size_t r)
{
if (a_len <= r)
{
r = a_len - 1;
}
if (l > r)
{
return;
}
for (size_t i = l; i <= r; i++)
{
if (i == r)
{
fprintf(stderr, "\033[1;36m%" PRId64 "\033[0m\n", a[i]);
}
else
{
fprintf(stderr, "\033[1;36m%" PRId64 "\033[0m ", a[i]);
}
}
}
void dump_u32_array_range(size_t a_len, u32 *a, size_t l, size_t r)
{
if (a_len <= r)
{
r = a_len - 1;
}
if (l > r)
{
return;
}
for (size_t i = l; i <= r; i++)
{
if (i == r)
{
fprintf(stderr, "\033[1;36m%" PRIu32 "\033[0m\n", a[i]);
}
else
{
fprintf(stderr, "\033[1;36m%" PRIu32 "\033[0m ", a[i]);
}
}
}
void dump_u64_array_range(size_t a_len, u64 *a, size_t l, size_t r)
{
if (a_len <= r)
{
r = a_len - 1;
}
if (l > r)
{
return;
}
for (size_t i = l; i <= r; i++)
{
if (i == r)
{
fprintf(stderr, "\033[1;36m%" PRIu64 "\033[0m\n", a[i]);
}
else
{
fprintf(stderr, "\033[1;36m%" PRIu64 "\033[0m ", a[i]);
}
}
}
void printb_32bit(u32 v)
{
u32 mask = (u32)1 << (sizeof(v) * CHAR_BIT - 1);
do
{
putchar_unlocked(mask & v ? '1' : '0');
} while (mask >>= 1);
}
void printb_64bit(u64 v)
{
u64 mask = (u64)1 << (sizeof(v) * CHAR_BIT - 1);
do
{
putchar_unlocked(mask & v ? '1' : '0');
} while (mask >>= 1);
}
u32 gcd32(u32 a, u32 b)
{
if (!a || !b)
return a | b;
u32 sh = CTZ32(a | b);
a >>= CTZ32(a);
do
{
b >>= CTZ32(b);
if (a > b)
SWAP(a, b);
b -= a;
} while (b);
return a << sh;
}
u64 gcd64(u64 a, u64 b)
{
if (!a || !b)
return a | b;
u64 sh = CTZ64(a | b);
a >>= CTZ64(a);
do
{
b >>= CTZ64(b);
if (a > b)
SWAP(a, b);
b -= a;
} while (b);
return a << sh;
}
typedef struct
{
i32 f, s;
u32 t;
} Bezout32;
typedef struct
{
i64 f, s;
u64 t;
} Bezout64;
PRIVATE Bezout32 bezout32(u32 x, u32 y)
{
bool swap = x < y;
if (swap)
SWAP(x, y);
if (y == 0)
{
if (x == 0)
return (Bezout32){0, 0, 0};
else if (swap)
return (Bezout32){0, 1, x};
else
return (Bezout32){1, 0, x};
}
i32 s0 = 1, s1 = 0, t0 = 0, t1 = 1;
while (true)
{
u32 q = x / y, r = x % y;
if (r == 0)
{
if (swap)
return (Bezout32){t1, s1, y};
else
return (Bezout32){s1, t1, y};
}
i32 s2 = s0 - (i32)(q)*s1, t2 = t0 - (i32)(q)*t1;
x = y, y = r;
s0 = s1, s1 = s2, t0 = t1, t1 = t2;
}
}
PRIVATE Bezout64 bezout64(u64 x, u64 y)
{
bool swap = x < y;
if (swap)
SWAP(x, y);
if (y == 0)
{
if (x == 0)
return (Bezout64){0, 0, 0};
else if (swap)
return (Bezout64){0, 1, x};
else
return (Bezout64){1, 0, x};
}
i64 s0 = 1, s1 = 0, t0 = 0, t1 = 1;
while (true)
{
u64 q = x / y, r = x % y;
if (r == 0)
{
if (swap)
return (Bezout64){t1, s1, y};
else
return (Bezout64){s1, t1, y};
}
i64 s2 = s0 - (i64)(q)*s1, t2 = t0 - (i64)(q)*t1;
x = y, y = r;
s0 = s1, s1 = s2, t0 = t1, t1 = t2;
}
}
PUBLIC u32 mod_inverse32(u32 x, u32 mod)
{
assert(gcd32(x, mod) == 1);
Bezout32 b = bezout32(x, mod);
assert(b.t == 1);
return b.f < 0 ? mod + b.f : (u32)b.f;
}
PUBLIC u64 mod_inverse64(u64 x, u64 mod)
{
assert(gcd64(x, mod) == 1);
Bezout64 b = bezout64(x, mod);
assert(b.t == 1);
return b.f < 0 ? mod + b.f : (u64)b.f;
}
PRIVATE u32 N_32, N2_32, NI_32, R1_32, R2_32, R3_32;
PUBLIC void Montgomery32(u32 mod)
{
assert(mod < 1073741824u);
N_32 = mod;
N2_32 = mod << 1;
NI_32 = mod;
NI_32 *= 2 - NI_32 * mod;
NI_32 *= 2 - NI_32 * mod;
NI_32 *= 2 - NI_32 * mod;
NI_32 *= 2 - NI_32 * mod;
R1_32 = (u32)(i32)-1 % mod + 1;
R2_32 = (u64)(i64)-1 % mod + 1;
R3_32 = (u32)(((u64)R1_32 * (u64)R2_32) % mod);
}
PUBLIC u32 get_mod32(void)
{
return N_32;
}
PUBLIC u32 get_dmod32(void)
{
return N2_32;
}
PUBLIC u32 get_one32(void)
{
return R1_32;
}
PRIVATE u32 mr32(u64 A)
{
u32 y = (u32)(A >> 32) - (u32)(((u64)((u32)A * NI_32) * N_32) >> 32);
return (i32)y < 0 ? y + N_32 : y;
}
PUBLIC u32 To32(u32 a)
{
return mr32((u64)a * R2_32);
}
PUBLIC u32 From32(u32 A)
{
return mr32((u64)A);
}
PUBLIC u32 Add32(u32 A, u32 B)
{
A += B - N2_32;
A += N2_32 & -(A >> 31);
return A;
}
PUBLIC u32 Sub32(u32 A, u32 B)
{
A -= B;
A += N2_32 & -(A >> 31);
return A;
}
PUBLIC u32 SAdd32(u32 A, u32 B)
{
A = A >= N_32 ? A % N_32 : A;
B = B >= N_32 ? B % N_32 : B;
A += B;
A -= (A >= N_32 ? N_32 : 0);
return A;
}
PUBLIC u32 SSub32(u32 A, u32 B)
{
A = A >= N_32 ? A % N_32 : A;
B = B >= N_32 ? B % N_32 : B;
A += (A < B ? N_32 : 0);
A -= B;
return A;
}
PUBLIC u32 Min32(u32 A)
{
return SSub32(0, A);
}
PUBLIC u32 Mul32(u32 A, u32 B)
{
return mr32((u64)A * B);
}
PUBLIC u32 Square32(u32 A)
{
return mr32((u64)A * A);
}
PUBLIC u32 Twice32(u32 A)
{
return (A <<= 1) >= N_32 ? A - N_32 : A;
}
PUBLIC u32 Power32(u32 A, size_t k)
{
return k ? Mul32(Power32(Square32(A), k >> 1), k & 1 ? A : R1_32) : R1_32;
}
PUBLIC u32 Inverse32(u32 A)
{
return mr32((u64)R3_32 * mod_inverse32(A, N_32));
}
PUBLIC u32 Div32(u32 A, u32 B)
{
return Mul32(A, Inverse32(B));
}
PUBLIC u32 Half32(u32 A)
{
return (A & 1) ? ((A >> 1) + (N_32 >> 1) + 1) : (A >> 1);
}
PUBLIC int Equal32(u32 A, u32 B)
{
return (((A >= N_32) ? (A - N_32) : A) == ((B >= N_32) ? (B - N_32) : B)) ? 1 : 0;
}
PUBLIC int NotEqual32(u32 A, u32 B)
{
return (((A >= N_32) ? (A - N_32) : A) != ((B >= N_32) ? (B - N_32) : B)) ? 1 : 0;
}
PUBLIC u32 In32(void)
{
u32 c = 0;
u32 a = 0;
while (c = getchar_unlocked(), c < 48 || c > 57)
;
while (47 < c && c < 58)
{
a = a * 10 + c - 48;
c = getchar_unlocked();
}
return To32(a);
}
PUBLIC void Out32(u32 A)
{
u32 a = From32(A);
out_u32(a);
}
PRIVATE u64 N_64, N2_64, NI_64, R1_64, R2_64, R3_64;
PUBLIC void Montgomery64(u64 mod)
{
assert(mod < 4611686018427387904ull);
N_64 = mod;
N2_64 = mod << 1;
NI_64 = mod;
NI_64 *= 2 - NI_64 * mod;
NI_64 *= 2 - NI_64 * mod;
NI_64 *= 2 - NI_64 * mod;
NI_64 *= 2 - NI_64 * mod;
NI_64 *= 2 - NI_64 * mod;
R1_64 = (u64)(i64)-1 % mod + 1;
R2_64 = (u128)(i128)-1 % mod + 1;
R3_64 = (u64)(((u128)R1_64 * (u128)R2_64) % mod);
}
PUBLIC u64 get_mod64(void)
{
return N_64;
}
PUBLIC u64 get_dmod64(void)
{
return N2_64;
}
PUBLIC u64 get_one64(void)
{
return R1_64;
}
PRIVATE u64 mr64(u128 A)
{
u64 y = (u64)(A >> 64) - (u64)(((u128)((u64)A * NI_64) * N_64) >> 64);
return (i64)y < 0 ? y + N_64 : y;
}
PUBLIC u64 To64(u64 a)
{
return mr64((u128)a * R2_64);
}
PUBLIC u64 From64(u64 A)
{
return mr64((u128)A);
}
PUBLIC u64 Add64(u64 A, u64 B)
{
A += B - N2_64;
A += N2_64 & -(A >> 63);
return A;
}
PUBLIC u64 Sub64(u64 A, u64 B)
{
A -= B;
A += N2_64 & -(A >> 63);
return A;
}
PUBLIC u64 SAdd64(u64 A, u64 B)
{
A = A >= N_64 ? A % N_64 : A;
B = B >= N_64 ? B % N_64 : B;
A += B;
A -= (A >= N_64 ? N_64 : 0);
return A;
}
PUBLIC u64 SSub64(u64 A, u64 B)
{
A = A >= N_64 ? A % N_64 : A;
B = B >= N_64 ? B % N_64 : B;
A += (A < B ? N_64 : 0);
A -= B;
return A;
}
PUBLIC u64 Min64(u64 A)
{
return SSub64(0, A);
}
PUBLIC u64 Mul64(u64 A, u64 B)
{
return mr64((u128)A * B);
}
PUBLIC u64 Square64(u64 A)
{
return mr64((u128)A * A);
}
PUBLIC u64 Twice64(u64 A)
{
return (A <<= 1) >= N_64 ? A - N_64 : A;
}
PUBLIC u64 Power64(u64 A, size_t k)
{
return k ? Mul64(Power64(Square64(A), k >> 1), k & 1 ? A : R1_64) : R1_64;
}
PUBLIC u64 Inverse64(u64 A)
{
return mr64((u128)R3_64 * mod_inverse64(A, N_64));
}
PUBLIC u64 Div64(u64 A, u64 B)
{
return Mul64(A, Inverse64(B));
}
PUBLIC u64 Half64(u64 A)
{
return (A & 1) ? ((A >> 1) + (N_64 >> 1) + 1) : (A >> 1);
}
PUBLIC int Equal64(u64 A, u64 B)
{
return (((A >= N_64) ? (A - N_64) : A) == ((B >= N_64) ? (B - N_64) : B)) ? 1 : 0;
}
PUBLIC int NotEqual64(u64 A, u64 B)
{
return (((A >= N_64) ? (A - N_64) : A) != ((B >= N_64) ? (B - N_64) : B)) ? 1 : 0;
}
PUBLIC u64 In64()
{
u64 c = 0;
u64 a = 0;
while (c = getchar_unlocked(), c < 48 || c > 57)
;
while (47 < c && c < 58)
{
a = a * 10 + c - 48;
c = getchar_unlocked();
}
return To64(a);
}
PUBLIC void Out64(u64 A)
{
u64 a = From64(A);
out_u64(a);
}
PRIVATE u64 m_b64, im_b64;
PRIVATE u64 divrem64[2] = {0};
PUBLIC void new_br64(u32 mod)
{
m_b64 = (u64)mod;
im_b64 = (~((u64)0ul)) / (u64)mod;
}
PUBLIC u32 get_mod_br32(void)
{
return (u32)m_b64;
}
PRIVATE void div_rem_br64(u64 lhs)
{
if (m_b64 == 1)
{
divrem64[0] = lhs;
divrem64[1] = 0;
return;
}
u64 q = (u64)(((u128)lhs * (u128)im_b64) >> 64);
u64 r = lhs - q * m_b64;
if (m_b64 <= r)
{
r -= m_b64;
q += 1ul;
}
divrem64[0] = q;
divrem64[1] = r;
}
PUBLIC u32 add_br32(u32 a, u32 b)
{
a = a >= m_b64 ? a - m_b64 : a;
b = b >= m_b64 ? b - m_b64 : b;
a += b;
a -= (a >= (u32)m_b64 ? (u32)m_b64 : 0);
return a;
}
PUBLIC u32 sub_br32(u32 a, u32 b)
{
a = a >= m_b64 ? a - m_b64 : a;
b = b >= m_b64 ? b - m_b64 : b;
a += (a < b ? (u32)m_b64 : 0);
a -= b;
return a;
}
PUBLIC u32 min_br32(u32 a)
{
return sub_br32(0, a);
}
PUBLIC u32 mul_br32(u32 a, u32 b)
{
div_rem_br64((u64)a * b);
return (u32)divrem64[1];
}
PUBLIC u32 square_br32(u32 a)
{
div_rem_br64((u64)a * a);
return (u32)divrem64[1];
}
PUBLIC u32 twice_br32(u32 a)
{
return mul_br32(a, 2);
}
PUBLIC u32 power_br32(u32 a, size_t k)
{
return k ? mul_br32(power_br32(square_br32(a), k >> 1), k & 1 ? a : 1) : 1;
}
PUBLIC u32 inverse_br32(u32 a)
{
if (gcd32(a, m_b64) != 1)
{
return 0;
}
return mod_inverse32(a, m_b64);
}
PUBLIC u32 div_br32(u32 a, u32 b)
{
u32 c = inverse_br32(b);
if (b == 0)
{
return (u32)(i32)-1;
}
return mul_br32(a, inverse_br32(b));
}
PUBLIC u32 half_br32(u32 a)
{
return (a & 1) ? ((a >> 1) + (m_b64 >> 1) + 1) : (a >> 1);
}
PRIVATE u128 m_b128, im_b128;
PRIVATE u128 divrem128[2] = {0};
PUBLIC void new_br128(u64 mod)
{
m_b128 = (u128)mod;
im_b128 = (~((u128)0ull)) / (u128)mod;
}
PUBLIC u64 get_mod_br64(void)
{
return (u64)m_b128;
}
PRIVATE void div_rem_br128(u128 lhs)
{
if (m_b128 == 1)
{
divrem128[0] = lhs;
divrem128[1] = 0;
return;
}
u128 t = (lhs >> 64) * (im_b128 >> 64);
u128 x = ((lhs & 0xffffffffffffffffull) * (im_b128 & 0xffffffffffffffffull)) >> 64;
u8 flag;
u128 auil = (lhs >> 64) * (im_b128 & 0xffffffffffffffffull);
if (auil <= (u128)((i128)(-1L)) - x)
flag = 0;
else
flag = 1;
x += auil;
t += flag;
u128 aliu = (lhs & 0xffffffffffffffffull) * (im_b128 >> 64);
if (aliu <= (u128)((i128)(-1L)) - x)
flag = 0;
else
flag = 1;
x += aliu;
t += flag;
u128 q = t + (x >> 64);
u128 r = lhs - q * m_b128;
if (m_b128 <= r)
{
r -= m_b128;
q += 1;
}
divrem128[0] = q;
divrem128[1] = r;
}
PUBLIC u64 add_br64(u64 a, u64 b)
{
a = a >= m_b128 ? a - m_b128 : a;
b = b >= m_b128 ? b - m_b128 : b;
a += b;
a -= (a >= (u64)m_b128 ? (u64)m_b128 : 0);
return a;
}
PUBLIC u64 sub_br64(u64 a, u64 b)
{
a = a >= m_b128 ? a - m_b128 : a;
b = b >= m_b128 ? b - m_b128 : b;
a += (a < b ? (u64)m_b128 : 0);
a -= b;
return a;
}
PUBLIC u64 min_br64(u64 a)
{
return sub_br64(0, a);
}
PUBLIC u64 mul_br64(u64 a, u64 b)
{
div_rem_br128((u128)a * b);
return (u64)divrem128[1];
}
PUBLIC u64 square_br64(u64 a)
{
div_rem_br128((u128)a * a);
return (u64)divrem128[1];
}
PUBLIC u64 twice_br64(u64 a)
{
return mul_br64(a, 2);
}
PUBLIC u64 power_br64(u64 a, size_t k)
{
return k ? mul_br64(power_br64(square_br64(a), k >> 1), k & 1 ? a : 1) : 1;
}
PUBLIC u64 inverse_br64(u64 a)
{
if (gcd64(a, m_b128) != 1)
{
return 0;
}
return mod_inverse64(a, m_b128);
}
PUBLIC u64 div_br64(u64 a, u64 b)
{
u64 c = inverse_br64(b);
if (b == 0)
{
return (u64)(i64)-1;
}
return mul_br64(a, inverse_br64(b));
}
PUBLIC u64 half_br64(u64 a)
{
return (a & 1) ? ((a >> 1) + (m_b128 >> 1) + 1) : (a >> 1);
}
int isqrt(u64 n)
{
if (n == 0)
return 0;
u64 a = n;
u64 b = 1;
u64 c;
if ((c = (a >> 32)) != 0)
{
a = c;
b <<= 16;
}
if ((c = (a >> 16)) != 0)
{
a = c;
b <<= 8;
}
if ((c = (a >> 8)) != 0)
{
a = c;
b <<= 4;
}
if ((c = (a >> 4)) != 0)
{
a = c;
b <<= 2;
}
if ((c = (a >> 2)) != 0)
{
a = c;
b <<= 1;
}
if (a <= 1)
b += b >> 1;
else
b <<= 1;
do
{
a = b;
b = (b + n / b) >> 1;
} while (b < a);
return (int)a;
}
enum isqrt_type
{
Floor = 0,
Ceil = 1,
Remain = 2,
};
static inline u64 floor_ceil_remain_isqrt(u64 x, enum isqrt_type mode)
{
static u64 x_floor_sqrt;
static u64 x_ceil_sqrt;
static u64 x_remain_sqrt;
if (x == 0)
return 0;
u32 lz = __builtin_clzll(x);
u64 n = 32 - (lz >> 1);
u64 s = (lz >> 1) << 1;
u64 t = n << 1;
u128 a = (u128)x;
u128 b = ((u128)1ull << 62) >> s;
u128 c = ((u128)1ull << 64) >> s;
u128 d = (((u128)1ull << 64) - 1) >> s;
u128 e = ((((u128)1ull << 64) - 1) << 65) >> s;
for (int _ = 0; _ < n; ++_)
{
if (a >= b)
{
a -= b;
b = ((b + b) & e) + c + (b & d);
}
else
{
b = ((b + b) & e) + (b & d);
}
a <<= 2;
}
x_floor_sqrt = b >> t;
x_ceil_sqrt = (a >> t) ? 1ull + (b >> t) : (b >> t);
x_remain_sqrt = a >> t;
if (mode == Floor)
{
return x_floor_sqrt;
}
else if (mode == Ceil)
{
return x_ceil_sqrt;
}
else
{
return x_remain_sqrt;
}
}
u64 floor_isqrt(u64 n)
{
return floor_ceil_remain_isqrt(n, Floor);
}
u64 ceil_isqrt(u64 n)
{
return floor_ceil_remain_isqrt(n, Ceil);
}
u64 remain_isqrt(u64 n)
{
return floor_ceil_remain_isqrt(n, Remain);
}
bool is_square(u64 n)
{
if (n <= 1)
return true;
if ((0x02030213u >> ((u32)n & 31)) & 1 != 1)
return false;
const u64 SQTABLE_MOD4095[64] = {0x2001002010213ul, 0x4200001008028001ul, 0x20000010004ul, 0x80200082010ul, 0x1800008200044029ul, 0x120080000010ul, 0x2200000080410400ul, 0x8100041000200800ul, 0x800004000020100ul, 0x402000400082201ul, 0x9004000040ul, 0x800002000880ul, 0x18002000012000ul, 0x801208ul, 0x26100000804010ul, 0x80000080000002ul, 0x108040040101045ul, 0x20c00004000102ul, 0x400000100c0010ul, 0x1300000040208ul, 0x804000020010000ul, 0x1008402002400080ul, 0x201001000200040ul, 0x4402000000806000ul, 0x10402000000ul, 0x1040008001200801ul, 0x4080000000020400ul, 0x10083080000002ul, 0x8220140000040000ul, 0x800084020100000ul, 0x80010400010000ul, 0x1200020108008060ul, 0x180000000ul, 0x400002400000018ul, 0x4241000200ul, 0x100800000000ul, 0x10201008400483ul, 0xc008000208201000ul, 0x800420000100ul, 0x2010002000410ul, 0x28041000000ul, 0x4010080000024ul, 0x400480010010080ul, 0x200040028000008ul, 0x100810084020ul, 0x20c0401000080000ul, 0x1000240000220000ul, 0x4000020800ul, 0x410000000480000ul, 0x8004008000804201ul, 0x806020000104000ul, 0x2080002000211000ul, 0x1001008001000ul, 0x20000010024000ul, 0x480200002040000ul, 0x48200044008000ul, 0x100000000010080ul, 0x80090400042ul, 0x41040200800200ul, 0x4000020100110ul, 0x2000400082200010ul, 0x1008200000000040ul, 0x2004800002ul, 0x2002010000080ul};
size_t p = n % 4095;
if ((SQTABLE_MOD4095[p >> 6] >> (p & 63)) & 1 != 1)
return false;
u64 newton_sqrt;
size_t k = 32 - (CLZ64(n - 1) >> 1);
u64 s = (u64)(1ul) << k;
u64 t = (s + (n >> k)) >> 1;
while (t < s)
{
s = t;
t = (s + n / s) >> 1;
}
newton_sqrt = s;
if (newton_sqrt * newton_sqrt != n)
return false;
return true;
}
int jacobi_symbol32(i32 a, i32 n)
{
int j = 1;
while (a)
{
if (a < 0)
{
a = -a;
if ((n & 3) == 3)
j = -j;
}
int s = CTZ32(a);
a >>= s;
if (((n & 7) == 3 || (n & 7) == 5) && (s & 1))
j = -j;
if ((a & n & 3) == 3)
j = -j;
SWAP(a, n);
a %= n;
if (a > n / 2)
a -= n;
}
return n == 1 ? j : 0;
}
int jacobi_symbol64(i64 a, i64 n)
{
int j = 1;
while (a)
{
if (a < 0)
{
a = -a;
if ((n & 3) == 3)
j = -j;
}
int s = CTZ64(a);
a >>= s;
if (((n & 7) == 3 || (n & 7) == 5) && (s & 1))
j = -j;
if ((a & n & 3) == 3)
j = -j;
SWAP(a, n);
a %= n;
if (a > n / 2)
a -= n;
}
return n == 1 ? j : 0;
}
PRIVATE bool _miller_rabin(u64 n, size_t bases_len, u64 bases[])
{
u64 s = CTZ64(n - 1);
u64 d = (n - 1) >> s;
Montgomery64(n);
for (size_t i = 0; i < bases_len; ++i)
{
if (n <= bases[i])
return true;
u64 a = Power64(To64(bases[i]), d);
if (a == get_one64())
continue;
u64 r = 1;
while (a != n - get_one64())
{
if (r == s)
return false;
a = Square64(a);
++r;
}
}
return true;
}
PRIVATE bool _miller_rabin_br(u64 n)
{
new_br128(n);
u64 s = CTZ64(n - 1);
u64 d = (n - 1) >> s;
u64 bases[7] = {2ul, 325ul, 9375ul, 28178ul, 450775ul, 9780504ul, 1795265022ul};
for (size_t i = 0; i < 7; ++i)
{
u64 a = power_br64(bases[i], d);
if (a == 1)
continue;
u64 r = 1;
while (a != n - 1)
{
if (r == s)
return false;
a = square_br64(a);
++r;
}
}
return true;
}
PUBLIC bool miller_rabin(u64 n)
{
if (n < 64ull)
return (1ull << n) & 2891462833508853932ull;
if (!(n & 1))
return false;
if (n < 1073741824ull)
{
u64 bases[3] = {2ul, 7ul, 61ul};
return _miller_rabin(n, 3, bases);
}
if (n < 4611686018427387904ull)
{
u64 bases[7] = {2ul, 325ul, 9375ul, 28178ul, 450775ul, 9780504ul, 1795265022ul};
return _miller_rabin(n, 7, bases);
}
return _miller_rabin_br(n);
}
PUBLIC bool baillie_psw(u64 n)
{
if (n < 64ull)
return (1ull << n) & 2891462833508853932ull;
if (!(n & 1))
return false;
new_br128(n);
{
u64 d = (n - 1) << CLZ64(n - 1);
u64 t = 2ull;
for (d <<= 1; d; d <<= 1)
{
t = square_br64(t);
if (d >> 63)
t = twice_br64(t);
}
if (t != 1)
{
u64 x = LSBit(n - 1);
u64 rev = n - 1;
for (x >>= 1; t != rev; x >>= 1)
{
if (x == 0)
return false;
t = square_br64(t);
}
}
}
{
i64 D = 5;
for (int i = 0; jacobi_symbol64(D, n) != -1 && i < 64; ++i)
{
if (i == 32 && is_square(n))
{
return false;
}
if (i & 1)
D -= 2;
else
D += 2;
D = -D;
}
u64 Q = (D < 0) ? ((1 - D) / 4 % n) : (n - (D - 1) / 4 % n);
u64 u = 1, v = 1, Qn = Q;
u64 k = (n + 1) << CLZ64(n + 1);
D %= (i64)n;
D = (D < 0) ? (D + n) : D;
for (k <<= 1; k; k <<= 1)
{
u = mul_br64(u, v);
v = sub_br64(square_br64(v), twice_br64(Qn));
Qn = square_br64(Qn);
if (k >> 63)
{
u64 uu = add_br64(u, v);
uu = half_br64(uu);
v = half_br64(add_br64(mul_br64(D, u), v));
u = uu;
Qn = mul_br64(Qn, Q);
}
}
if (u == 0 || v == 0)
return true;
u64 x = (n + 1) & ~n;
for (x >>= 1; x; x >>= 1)
{
u = mul_br64(u, v);
v = sub_br64(square_br64(v), twice_br64(Qn));
if (v == 0)
return true;
Qn = square_br64(Qn);
}
}
return false;
}
int main(int argc, char *argv[])
{
int Q = in_i32();
while (Q--)
{
u64 x = in_u64();
out_u64(x);
SP();
putchar_unlocked(miller_rabin(x) ? '1' : '0');
NL();
}
return 0;
}