2022 Henan Mengxin League game (3): Henan University L - synthetic game

L - Synthetic games

• Time complexity $O(t\times log(n))$

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

typedef long long LL;
const int N = 100010, MOD = 1e9 + 7;
int fac[N],inv[N];

int main()
{
    
	fac[0]=inv[0]=1;
	for(int i=1;i<=100000;i++) fac[i]=(LL)fac[i-1]*i%MOD;
	for(int i=1;i<=100000;i++) inv[i]=(LL)inv[i-1]*500000004%MOD;
		
	int T;cin>>T;
	while(T--)
	{
    
		int n;cin>>n;
		int res=fac[n];
		while(n)
		{
    
			n>>=1;
			res=(LL)res*inv[n]%MOD;
		}
		cout<<res<<endl;
	}
	return 0;
}