牛客OI赛制测试赛2 F ：假的数学游戏

#include<bits/stdc++.h>
using namespace std;

const double PI=3.1415926;
typedef long long LL;

int main(){
  
  LL x;
  scanf("%lld",&x);
  LL l=10,r=1LL<<40,node;
  double key=log(x)*x;
  while(l<=r){
    
    LL mid=(l+r)>>1;
    if(log(sqrt(2*PI*mid))+mid*(log(mid)-1)>key) node=mid,r=mid-1;
    else l=mid+1;
  } 
  printf("%lld\n",node);
}