#include #include #include typedef __int128 int128_t; typedef unsigned __int128 uint128_t; char ibuf[300000]; char *ibufe = ibuf-1; char buf[300000]; char *bufe = buf; static inline void readall(){ int k, t = 0; while((k=read(STDIN_FILENO, ibuf+t, sizeof(ibuf)-t))>0) t += k; } static inline uint64_t read_uintll(){ uint64_t x=0; while(*(++ibufe) <'0'); do { x *= 10; x += *ibufe-'0'; } while(*(++ibufe) >='0'); return x; } static inline uint64_t readwrite_uintll(){ uint64_t x=0; while(*(++ibufe) <'0'); do { x *= 10; x += *ibufe-'0'; *bufe++ = *ibufe; } while(*(++ibufe) >='0'); *bufe++ = ' '; return x; } static inline void write_bitln(int x){ *bufe++ = '0'+x; *bufe++ = '\n'; } static inline void writeall(){ int k, t = 0; while((k=write(STDOUT_FILENO, buf+t, bufe-buf-t))>0) t += k; } static inline uint64_t ex_gcd(uint64_t y){ int i; uint64_t u, v; u = 1; v = 0; uint64_t x = 1LL<<63; for(i=0;i<64;i++){ if(u&1){ u = (u + y) / 2; v = v/2 + x; } else { u >>= 1; v >>= 1; } } return -v; } static inline uint64_t MR(uint128_t x, uint64_t m, uint64_t n){ int64_t z = (x >> 64) - ((((uint64_t) x * m) * (uint128_t) n) >> 64); return z < 0 ? z + n : z; } static inline uint64_t RM(uint64_t x, uint64_t r2, uint64_t m, uint64_t n){ return MR((uint128_t) r2 * x, m, n); } static inline uint64_t mulmod64(uint64_t x, uint64_t y, uint64_t m, uint64_t n){ return MR((uint128_t) x*y, m, n); } int jacobi(int64_t a, uint64_t n){ uint64_t t; int j = 1; while(a){ if(a<0){ a = -a; if((n&3)==3) j = -j; } int ba = __builtin_ctzll(a); a >>= ba; if(((n&7)==3||(n&7)==5) && (ba&1)) j = -j; if((a&n&3)==3) j = -j; t = a; a = n; n = t; a %= n; if(a>n/2) a-=n; } return n == 1 ? j : 0; } static inline uint64_t addmod64(uint64_t x, uint64_t y, uint64_t n){ return x + y >= n ? x + y - n : x + y; } static inline uint64_t submod64(uint64_t x, uint64_t y, uint64_t n){ return x >= y ? x - y : x - y + n; } int is_prime64(const uint64_t n){ if(n <= 1) return 0; if(n <= 3) return 1; if(!(n & 1)) return 0; const uint64_t one = -1ULL % n + 1; const uint64_t r2 = (uint128_t) (int128_t) -1 % n + 1; const uint64_t m = ex_gcd(n); { uint64_t d = (n-1) << __builtin_clzll(n-1); uint64_t t = one << 1; if(t >= n) t -= n; for(d<<=1;d;d<<=1){ t = mulmod64(t, t, m, n); if(d>>63){ t <<= 1; if(t>=n) t -= n; } } if(t != one){ uint64_t x = (n-1) & -(n-1); uint64_t mone = n - one; for(x>>=2;t!=mone;x>>=1){ if(x == 0) return 0; t = mulmod64(t, t, m, n); // if(t == one) return 0; } } } { int64_t D = 5; int i; for(i=0;jacobi(D, n) != -1 && i<64;i++){ if(i==32){ uint32_t k = round(sqrtl(n)); if(k*k == n) return 0; } if(i&1) D -= 2; else D += 2; D = -D; } // if(i==64) puts("ERROR"); uint64_t Q = RM(D < 0 ? (1-D)/4%n : n - (D-1)/4%n, r2, m, n); uint64_t u, v, Qn; uint64_t k = (n+1) << __builtin_clzll(n+1); u = one; v = one; Qn = Q; D %= (int64_t) n; D = RM(D < 0 ? n+D : D, r2, m, n); for(k<<=1;k;k<<=1){ u = mulmod64(u,v,m,n); v = submod64(mulmod64(v,v,m,n), addmod64(Qn, Qn, n), n); Qn = mulmod64(Qn, Qn, m, n); if(k>>63){ uint64_t uu = addmod64(u, v, n); if(uu&1) uu += n; uu >>= 1; v = addmod64(mulmod64(D,u,m,n), v, n); if(v&1) v += n; v >>= 1; u = uu; Qn = mulmod64(Qn, Q, m, n); } } if(u == 0 || v == 0) return 1; uint64_t x = (n+1) & ~n; for(x>>=2;x;x>>=1){ u = mulmod64(u,v,m,n); v = submod64(mulmod64(v,v,m,n), addmod64(Qn, Qn, n), n); if(v == 0) return 1; Qn = mulmod64(Qn, Qn, m, n); } } return 0; } int main(){ int i, n; readall(); n = read_uintll(); for(i=0;i