/+ dub.sdl: name "A" dependency "dcomp" version=">=0.7.1" +/ import std.stdio, std.algorithm, std.range, std.conv; // import dcomp.foundation, dcomp.scanner; // import dcomp.numeric.prime; long cnt(long n, long p) { long sm = 0; long q = p; while (p <= n) { sm += n / p; p *= q; } return sm; } long divc(long n, long m) { auto f = factorList(m).group; // writeln(f); long ans = 10L^^18; foreach (pr; f) { long c = cnt(n, pr[0]); ans = min(ans, c / pr[1]); } return ans; } import std.math; int main() { Scanner sc = new Scanner(stdin); long n, m; sc.read(n, m); // writeln(divc(n, m)); real f = 0; f += log10(2 * PI * n) / 2 + n * log10(n / E); f += log10(1 + 1.0/12.0/n + 1.0/288.0/n/n); // f += n * log(n) - n; f -= divc(n, m) * log10(m); // writeln(f); real d = floor(f); f -= d; writefln("%fe%d", pow(10, f), d.to!long); // writefln("%e", pow(10, f)); return 0; } /* IMPORT /home/yosupo/Program/dcomp/source/dcomp/foundation.d */ // module dcomp.foundation; static if (__VERSION__ <= 2070) { /* Copied by https://github.com/dlang/phobos/blob/master/std/algorithm/iteration.d Copyright: Andrei Alexandrescu 2008-. License: $(HTTP boost.org/LICENSE_1_0.txt, Boost License 1.0). */ template fold(fun...) if (fun.length >= 1) { auto fold(R, S...)(R r, S seed) { import std.algorithm : reduce; static if (S.length < 2) { return reduce!fun(seed, r); } else { import std.typecons : tuple; return reduce!fun(tuple(seed), r); } } } } version (X86) static if (__VERSION__ < 2071) { import core.bitop : bsf, bsr, popcnt; int bsf(ulong v) { foreach (i; 0..64) { if (v & (1UL << i)) return i; } return -1; } int bsr(ulong v) { foreach_reverse (i; 0..64) { if (v & (1UL << i)) return i; } return -1; } int popcnt(ulong v) { int c = 0; foreach (i; 0..64) { if (v & (1UL << i)) c++; } return c; } } /* IMPORT /home/yosupo/Program/dcomp/source/dcomp/scanner.d */ // module dcomp.scanner; // import dcomp.array; class Scanner { import std.stdio : File; import std.conv : to; import std.range : front, popFront, array, ElementType; import std.array : split; import std.traits : isSomeChar, isStaticArray, isArray; import std.algorithm : map; File f; this(File f) { this.f = f; } char[512] lineBuf; char[] line; private bool succW() { import std.range.primitives : empty, front, popFront; import std.ascii : isWhite; while (!line.empty && line.front.isWhite) { line.popFront; } return !line.empty; } private bool succ() { import std.range.primitives : empty, front, popFront; import std.ascii : isWhite; while (true) { while (!line.empty && line.front.isWhite) { line.popFront; } if (!line.empty) break; line = lineBuf[]; f.readln(line); if (!line.length) return false; } return true; } private bool readSingle(T)(ref T x) { import std.algorithm : findSplitBefore; import std.string : strip; import std.conv : parse; if (!succ()) return false; static if (isArray!T) { alias E = ElementType!T; static if (isSomeChar!E) { auto r = line.findSplitBefore(" "); x = r[0].strip.dup; line = r[1]; } else static if (isStaticArray!T) { foreach (i; 0..T.length) { bool f = succW(); assert(f); x[i] = line.parse!E; } } else { FastAppender!(E[]) buf; while (succW()) { buf ~= line.parse!E; } x = buf.data; } } else { x = line.parse!T; } return true; } int read(T, Args...)(ref T x, auto ref Args args) { if (!readSingle(x)) return 0; static if (args.length == 0) { return 1; } else { return 1 + read(args); } } } /* IMPORT /home/yosupo/Program/dcomp/source/dcomp/array.d */ // module dcomp.array; T[N] fixed(T, size_t N)(T[N] a) {return a;} struct FastAppender(A) { import std.algorithm : max; import std.range.primitives : ElementEncodingType; import core.stdc.string : memcpy; private alias T = ElementEncodingType!A; private T* _data; private size_t len, cap; @property size_t length() const {return len;} bool empty() const { return len == 0; } void reserve(size_t nlen) { import core.memory : GC; if (nlen <= cap) return; void* nx = GC.malloc(nlen * T.sizeof); cap = nlen; if (len) memcpy(nx, _data, len * T.sizeof); _data = cast(T*)(nx); } void opOpAssign(string op : "~")(T item) { if (len == cap) { reserve(max(4, cap*2)); } _data[len++] = item; } void insertBack(T item) { this ~= item; } void removeBack() { len--; } void clear() { len = 0; } ref inout(T) back() inout { assert(len); return _data[len-1]; } T[] data() { return (_data) ? _data[0..len] : null; } } /* IMPORT /home/yosupo/Program/dcomp/source/dcomp/numeric/prime.d */ // module dcomp.numeric.prime; T[] divisorList(T)(T x) { import std.algorithm : sort; T[] res; for (T i = 1; i*i <= x; i++) { if (x%i == 0) { res ~= i; if (i*i != x) res ~= x/i; } } sort(res); return res; } T[] factorList(T)(T x) { T[] res; for (T i = 2; i*i <= x; i++) { while (x % i == 0) { res ~= i; x /= i; } } if (x > 1) res ~= x; return res; } /* This source code generated by dcomp and include dcomp's source code. dcomp's Copyright: Copyright (c) 2016- Kohei Morita. (https://github.com/yosupo06/dcomp) dcomp's License: MIT License(https://github.com/yosupo06/dcomp/blob/master/LICENSE.txt) */