#pragma region opt #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma endregion opt #pragma region header #define _GNU_SOURCE #include #include #include #include #include #include #include #include #include #pragma endregion header #pragma region type /* signed integer */ typedef int8_t i8; typedef int16_t i16; typedef int32_t i32; typedef int64_t i64; typedef __int128_t i128; /* unsigned integer */ typedef uint8_t u8; typedef uint16_t u16; typedef uint32_t u32; typedef uint64_t u64; typedef __uint128_t u128; /* floating point number */ typedef float f32; typedef double f64; typedef long double f80; #pragma endregion type #pragma region macro #define MIN(a, b) (((a) < (b)) ? (a) : (b)) #define MAX(a, b) (((a) > (b)) ? (a) : (b)) #define SWAP(a, b) (((a) ^= (b)), ((b) ^= (a)), ((a) ^= (b))) #define POPCNT32(a) __builtin_popcount((a)) #define POPCNT64(a) __builtin_popcountll((a)) #define CTZ32(a) __builtin_ctz((a)) #define CLZ32(a) __builtin_clz((a)) #define CTZ64(a) __builtin_ctzll((a)) #define CLZ64(a) __builtin_clzll((a)) #define HAS_SINGLE_BIT32(a) (__builtin_popcount((a)) == (1)) #define HAS_SINGLE_BIT64(a) (__builtin_popcountll((a)) == (1)) #define MSB32(a) ((31) - __builtin_clz((a))) #define MSB64(a) ((63) - __builtin_clzll((a))) #define BIT_WIDTH32(a) ((a) ? ((32) - __builtin_clz((a))) : (0)) #define BIT_WIDTH64(a) ((a) ? ((64) - __builtin_clzll((a))) : (0)) #define LSBit(a) ((a) & (-(a))) #define CLSBit(a) ((a) & ((a) - (1))) #define BIT_CEIL32(a) ((!(a)) ? (1) : ((POPCNT32(a)) == (1) ? ((1u) << ((31) - CLZ32((a)))) : ((1u) << ((32) - CLZ32(a))))) #define BIT_CEIL64(a) ((!(a)) ? (1) : ((POPCNT64(a)) == (1) ? ((1ull) << ((63) - CLZ64((a)))) : ((1ull) << ((64) - CLZ64(a))))) #define BIT_FLOOR32(a) ((!(a)) ? (0) : ((1u) << ((31) - CLZ32((a))))) #define BIT_FLOOR64(a) ((!(a)) ? (0) : ((1ull) << ((63) - CLZ64((a))))) #define _ROTL32(x, s) (((x) << ((s) % (32))) | (((x) >> ((32) - ((s) % (32)))))) #define _ROTR32(x, s) (((x) >> ((s) % (32))) | (((x) << ((32) - ((s) % (32)))))) #define ROTL32(x, s) (((s) == (0)) ? (x) : ((((i64)(s)) < (0)) ? (_ROTR32((x), -(s))) : (_ROTL32((x), (s))))) #define ROTR32(x, s) (((s) == (0)) ? (x) : ((((i64)(s)) < (0)) ? (_ROTL32((x), -(s))) : (_ROTR32((x), (s))))) #define _ROTL64(x, s) (((x) << ((s) % (64))) | (((x) >> ((64) - ((s) % (64)))))) #define _ROTR64(x, s) (((x) >> ((s) % (64))) | (((x) << ((64) - ((s) % (64)))))) #define ROTL64(x, s) (((s) == (0)) ? (x) : ((((i128)(s)) < (0)) ? (_ROTR64((x), -(s))) : (_ROTL64((x), (s))))) #define ROTR64(x, s) (((s) == (0)) ? (x) : ((((i128)(s)) < (0)) ? (_ROTL64((x), -(s))) : (_ROTR64((x), (s))))) #pragma endregion macro #pragma region io int read_int(void) { // -2147483648 ~ 2147483647 (> 10 ^ 9) int 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; } i32 in_i32(void) { // -2147483648 ~ 2147483647 (> 10 ^ 9) 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; } u32 in_u32(void) { // 0 ~ 4294967295 (> 10 ^ 9) 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; } i64 in_i64(void) { // -9223372036854775808 ~ 9223372036854775807 (> 10 ^ 18) 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; } u64 in_u64(void) { // 0 ~ 18446744073709551615 (> 10 ^ 19) 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; } static inline void write_int_inner(int x) { if (x >= 10) write_int_inner(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); } void write_int(int x) { if (x < 0) { putchar_unlocked('-'); x = -x; } write_int_inner(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); } void out_u32(u32 x) { if (x >= 10) out_u32(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); } 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); } void out_u64(u64 x) { if (x >= 10) out_u64(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); } void NL(void) { putchar_unlocked('\n'); } void SP(void) { putchar_unlocked(' '); } void write_int_array(int *a, int a_len) { for (int i = 0; i < a_len; i++) { if (i) SP(); write_int(a[i]); } NL(); } void out_i32_array(i32 *a, int a_len) { for (int i = 0; i < a_len; i++) { if (i) SP(); out_i32(a[i]); } NL(); } void out_u32_array(u32 *a, int a_len) { for (int i = 0; i < a_len; i++) { if (i) SP(); out_u32(a[i]); } NL(); } void out_i64_array(i64 *a, int a_len) { for (int i = 0; i < a_len; i++) { if (i) SP(); out_i64(a[i]); } NL(); } void out_u64_array(u64 *a, int a_len) { for (int i = 0; i < a_len; i++) { if (i) SP(); out_u64(a[i]); } NL(); } #pragma endregion io #pragma region m32 typedef uint32_t m32; static inline m32 get_n2_m32(u32 mod) { return (-(u64)mod) % mod; } static inline m32 get_r_m32(u32 mod) { u32 ret = mod; for (int i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static inline m32 reduce_m32(u64 b, m32 r, u32 mod) { return (b + (u64)((u32)b * (u32)(-r)) * mod) >> 32; } static inline m32 to_m32(i64 b, m32 n2, m32 r, u32 mod) { return reduce_m32((u64)(b % mod + mod) * n2, r, mod); } static inline u32 from_m32(m32 a, m32 r, u32 mod) { u32 ret = reduce_m32((u64)a, r, mod); return ret >= mod ? ret - mod : ret; } static inline m32 add_m32(m32 a, m32 b, u32 mod) { m32 ret = a; if ((i32)(ret += b - 2 * mod) < 0) ret += 2 * mod; return ret; } static inline m32 sub_m32(m32 a, m32 b, u32 mod) { m32 ret = a; if ((i32)(ret -= b) < 0) ret += 2 * mod; return ret; } static inline m32 min_m32(m32 a, u32 mod) { return sub_m32(0, a, mod); } static inline m32 mul_m32(m32 a, m32 b, m32 r, u32 mod) { m32 ret = reduce_m32((u64)a * b, r, mod); return ret; } static inline m32 pow_m32(m32 a, u64 n, m32 n2, m32 r, u32 mod) { m32 ret = to_m32(1, n2, r, mod); m32 mul = a; while (n > 0) { if (n & 1) ret = mul_m32(ret, mul, r, mod); mul = mul_m32(mul, mul, r, mod); n >>= 1; } return ret; } static inline m32 recip_m32(m32 a, m32 n2, m32 r, u32 mod) { return pow_m32(a, mod - 2, n2, r, mod); } static inline m32 div_m32(m32 a, m32 b, m32 n2, m32 r, u32 mod) { return mul_m32(a, recip_m32(b, n2, r, mod), r, mod); } m32 in_m32(m32 n2, m32 r, u32 mod) { u32 ret = in_u32(); return to_m32((i64)ret, n2, r, mod); } void out_m32(m32 a, m32 r, u32 mod) { u32 ret = from_m32(a, r, mod); out_u32(ret); } #pragma endregion m32 #pragma region m64 typedef uint64_t m64; static inline m64 get_n2_m64(u64 mod) { return (-(u128)mod) % mod; } static inline m64 get_r_m64(u64 mod) { u64 ret = mod; for (int i = 0; i < 5; ++i) ret *= 2 - mod * ret; return ret; } static inline m64 reduce_m64(u128 b, m64 r, u64 mod) { return (b + (u128)((u64)b * (u64)(-r)) * mod) >> 64; } static inline m64 to_m64(i128 b, m64 n2, m64 r, u64 mod) { return reduce_m64(((u128)b + mod) * n2, r, mod); } static inline u64 from_m64(m64 a, m64 r, u64 mod) { u64 ret = reduce_m64((u128)a, r, mod); return ret >= mod ? ret - mod : ret; } static inline m64 add_m64(m64 a, m64 b, u64 mod) { m64 ret = a; if ((i64)(ret += b - 2 * mod) < 0) ret += 2 * mod; return ret; } static inline m64 sub_m64(m64 a, m64 b, u64 mod) { m64 ret = a; if ((i64)(ret -= b) < 0) ret += 2 * mod; return ret; } static inline m64 min_m64(m64 a, u64 mod) { return sub_m64(0, a, mod); } static inline m64 mul_m64(m64 a, m64 b, m64 r, u64 mod) { m64 ret = reduce_m64((u128)a * b, r, mod); return ret; } static inline m64 pow_m64(m64 a, u64 n, m64 n2, m64 r, u64 mod) { m64 ret = to_m64(1, n2, r, mod); m64 mul = a; while (n > 0) { if (n & 1) ret = mul_m64(ret, mul, r, mod); mul = mul_m64(mul, mul, r, mod); n >>= 1; } return ret; } static inline m64 recip_m64(m64 a, m64 n2, m64 r, u64 mod) { return pow_m64(a, mod - 2, n2, r, mod); } static inline m64 div_m64(m64 a, m64 b, m64 n2, m64 r, u64 mod) { return mul_m64(a, recip_m64(b, n2, r, mod), r, mod); } m64 in_m64(m64 n2, m64 r, u64 mod) { u64 ret = in_u64(); return to_m64((i128)ret, n2, r, mod); } void out_m64(m64 a, m64 r, u64 mod) { u64 ret = from_m64(a, r, mod); out_u64(ret); } #pragma endregion m64 #pragma region miller_rabin_primary_test bool is_prime32(u32 n) { u32 m = n - 1; m32 n2 = get_n2_m32(n); m32 r = get_r_m32(n); m32 one = to_m32(1, n2, r, n); m32 rev = to_m32(m, n2, r, n); u32 d = m >> CTZ32(m); u32 base[] = { 2u, 7u, 61u }; for (int i = 0; i < 3; i++) { if (n <= base[i]) break; u32 t = d; m32 y = pow_m32(to_m32(base[i], n2, r, n), t, n2, r, n); while (t != m && y != one && y != rev) { y = mul_m32(y, y, r, n); t <<= 1; } if (y != rev && (!(t & 1))) return false; } return true; } bool is_prime64(u64 n) { u64 m = n - 1; m64 n2 = get_n2_m64(n); m64 r = get_r_m64(n); m64 one = to_m64(1, n2, r, n); m64 rev = to_m64(m, n2, r, n); u64 d = m >> CTZ64(m); u64 base[] = { 2ul, 325ul, 9375ul, 28178ul, 450775ul, 9780504ul, 1795265022ul }; for (int i = 0; i < 7; i++) { if (n <= base[i]) break; u64 t = d; m64 y = pow_m64(to_m64(base[i], n2, r, n), t, n2, r, n); while (t != m && y != one && y != rev) { y = mul_m64(y, y, r, n); t <<= 1; } if (y != rev && (!(t & 1))) return false; } return true; } bool is_prime(u64 n) { if (n <= 3ul) return n == 2ul || n == 3ul; if (!(n & 1)) return false; if (n < ((u32)1u << 30)) return is_prime32((u32)n); return is_prime64(n); } #pragma endregion miller_rabin_primary_test void Main(void) { int n = read_int(); while (n--) { u64 x = in_u64(); out_u64(x); SP(); write_int(is_prime(x)); NL(); } } int main(void) { Main(); return 0; }