#include "bits/stdc++.h" #include using namespace std; typedef long long ll; typedef unsigned long long ull; typedef vector veci; typedef vector vecll; typedef vector vecs; template using Hash=unordered_map; #define REP(i, a, n) for(ll i = a; i < (ll)n; i++) #define RREP(i, a, n) for(ll i = n-1; i >= (ll)a; i--) #define rep(i, n) REP(i, 0, n) #define rrep(i, n) RREP(i, 0, n) #define MD 1000000007 template T read(){T a;cin >> a;return a;} template void read(T& a){cin >> a;} template void read(T& a, Args&... args){cin >> a; read(args...);} template void rarr(T a, int n){for(int i = 0; i < n; i++) {cin >> a[i];}} template void write(T a){cout << setprecision(15) << a << endl;} template void write(T a, Args... args){cout << setprecision(15) << a << c; write(args...);} template void warr(vector a, const char* c = " "){cout << a[0];for(int i = 1; i < (int)a.size(); i++)cout << c << a[i];cout << endl;} template void warr(T a, int n, const char* c = " "){cout << a[0];for(int i = 1; i < n; i++)cout << c << a[i];cout << endl;} void split(string s, string delim, veci& result){result.clear();string::size_type pos = 0;while(pos != string::npos){string::size_type p = s.find(delim, pos);if(p == string::npos){result.push_back(atoi(s.substr(pos).data()));break;}else {result.push_back(atoi(s.substr(pos, p - pos).data()));}pos = p + delim.size();}} void split(string s, string delim, vecs& result){result.clear();string::size_type pos = 0;while(pos != string::npos){string::size_type p = s.find(delim, pos);if(p == string::npos){result.push_back(s.substr(pos));break;}else {result.push_back(s.substr(pos, p - pos));}pos = p + delim.size();}} inline ll gcd(ll a, ll b){while(true) {ll k = a % b;if(k == 0)return b;a = b;b = k;}} inline ll lcm(ll a, ll b){return a*b/gcd(a,b);} ll comb(ll n, ll m){ll p=1;m=min(m,n-m);for(ll i=1;i<=m;i++){p*=n-i+1;p/=i;}return p;} int prime(veci& v, int n) { bool p[5000001] = {1, 1}; for(int i = 2; i <= n; i++) { if(p[i]) continue; v.push_back(i); for(int j = i * 2; j <= n; j += i) p[j] = true; } return v.size(); } int main(void) { ll n,m; read(n,m); ll mp=1e9; ll sm=sqrt(m); veci pm; prime(pm,sm); vector pf; ll tm=m; for(auto it:pm){ if(m%it!=0)continue; while(tm%it==0)tm/=it; pf.push_back(it); } if(tm!=1)pf.push_back(tm); for(auto it:pf){ ll tn=n; ll tm=m; int ct=0; ll t_mp=0; while(tn>0)t_mp+=tn/it,tn/=it; while(tm%it==0)tm/=it,ct++; mp=min(mp,t_mp/ct); } long double p=log10l(sqrt(2.0*M_PI*n)); p+=n*log10l(n/exp(1.0)); p+=log10l(1.0+1.0/(12.0*n)); p-=mp*log10l(m); cout<