#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){ uint64_t z = ((uint128_t) ((uint64_t) x * m) * n + x) >> 64; return z < n ? z : z - n; } 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); } static inline uint64_t modpow64(uint64_t a, uint64_t k, uint64_t m, uint64_t n){ uint64_t r; for(r=a,--k;k;k/=2){ if(k&1) r = mulmod64(r, a, m, n); a = mulmod64(a, a, m, n); } return r; } 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%8==3||n%8==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; } void lucasmod(uint64_t k, uint64_t m, uint64_t n, uint64_t q, uint64_t *u, uint64_t *v, uint64_t *pq){ uint64_t a, b, c, d, ux, uy, vx, vy, r; uint64_t one = -1ULL % n + 1; uint64_t two = addmod64(one, one, n); a = one; b = n-q; c = one; d = 0; ux = 0; uy = one; vx = two; vy = one; r = q; *pq = one; for(;k;k/=2){ if(k&1){ uint64_t uyy = addmod64(mulmod64(a,uy,m,n), mulmod64(b,ux,m,n), n) ; ux = addmod64(mulmod64(c,uy,m,n), mulmod64(d,ux,m,n), n); uy = uyy; uint64_t vyy = addmod64(mulmod64(a,vy,m,n), mulmod64(b,vx,m,n), n); vx = addmod64(mulmod64(c,vy,m,n), mulmod64(d,vx,m,n), n); vy = vyy; *pq = mulmod64(r,*pq,m,n); } uint64_t aa = addmod64(mulmod64(a,a,m,n), mulmod64(b,c,m,n), n); uint64_t bb = addmod64(mulmod64(a,b,m,n), mulmod64(b,d,m,n), n); uint64_t cc = addmod64(mulmod64(c,a,m,n), mulmod64(d,c,m,n), n); uint64_t dd = addmod64(mulmod64(c,b,m,n), mulmod64(d,d,m,n), n); a = aa; b = bb; c = cc; d = dd; r = mulmod64(r,r,m,n); } *u = ux; *v = vx; } /* static inline uint64_t modpow64_o(uint64_t a, uint64_t k, uint64_t n){ uint64_t r; for(r=1;k;k/=2){ if(k&1) r = mulmod64(r,a,n); a = mulmod64(a,a,n); } return r; } */ int is_prime64(const uint64_t n){ // static const uint32_t ps[] = {3, 7, 11, 13, 17, 19}; int i, j, r; uint64_t d, one, r2, m; if(n <= 1) return 0; if(n <= 3) return 1; if(!(n & 1)) return 0; /* for(i=0;i> r; mone = n - one; a = one << 1; if(a >= n) a -= n; if(a == 0) return 1; t = modpow64(a, d, m, n); if(t != one){ for(j=0;t!=mone;j++){ if(j == r-1) return 0; t = MR((uint128_t) t * t, m, n); // if(t == one) return 0; } } } { int64_t D = 5; for(i=0;jacobi(D, n) != -1 && i<64;i++){ if(i==16){ 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 d = (n+1) >> __builtin_ctzll(n+1); uint64_t u, v, Qn; lucasmod(d, m, n, Q, &u, &v, &Qn); if(u == 0 || v == 0) return 1; for(;d