// yukicoder: No.575 n! / m / m / m... // 2019.4.20 bal4u #include #include #define SIZE 50 long long factor[SIZE]; int power[SIZE]; int ptbl[] = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 0 }; int prime_factor(long long n) { int i, d, sz; int *pp; sz = 0; if ((n & 1) == 0) { factor[sz] = 2; do n >>= 1, power[sz]++; while ((n & 1) == 0); sz++; } for (pp = ptbl; n > 1 && *pp > 0; pp++) { if (n % *pp) continue; d = *pp; factor[sz] = d; do n /= d, power[sz]++; while (n % d == 0); sz++; } if (n > 1) { int b = (int)sqrt((double)n); for (i = 1009; n > 1; i += 2) { if (i > b) { factor[sz] = n, power[sz++] = 1; break; } if (n % i == 0) { factor[sz] = i; do n /= i, power[sz]++; while (n % i == 0); sz++; } } } return sz; } #define PI 3.1415926535897932384626433832795 #define E 2.7182818284590452353602874713526 double calc(int n, long long m, long long c) { int i; double a = 0; for (i = 2; i <= n; i++) a += log10((double)i); return a - c*log10((double)m); } long long check(long long n, long long f, int p) { long long c = 0, d = f; while (d <= n) c += n/d, d *= f; return c / p; } int main() { int i, sz; long long n, m, c, d; double p; scanf("%lld%lld", &n, &m); sz = prime_factor(m); c = 0x7fffffffffffffLL; for (i = 0; i < sz; i++) { d = check(n, factor[i], power[i]); if (d < c) c = d; } if (n <= 1000) p = calc((int)n, m, c); else p = 0.5*log10(2*PI*n) + n*log10(n/E) + log10(1 + 1/(12.0*n)) - c*log10((double)m); d = (long long)(p+1e-8); p -= d; p = pow(10, p); printf("%lfe%lld\n", p, d); return 0; }