Fansblog HDU

Farmer John keeps a website called ‘FansBlog’ .Everyday , there are many people visited this blog.One day, he find the visits has reached P , which is a prime number.He thinks it is a interesting fact.And he remembers that the visits had reached another prime number.He try to find out the largest prime number Q ( Q < P ) ,and get the answer of Q! Module P.But he is too busy to find out the answer. So he ask you for help. ( Q! is the product of all positive integers less than or equal to n: n! = n * (n-1) * (n-2) * (n-3) *… * 3 * 2 * 1 . For example, 4! = 4 * 3 * 2 * 1 = 24 )

Input

First line contains an number T(1<=T<=10) indicating the number of testcases.
Then T line follows, each contains a positive prime number P (1e9≤p≤1e14)

Output

For each testcase, output an integer representing the factorial of Q modulo P.

Sample Input

1
1000000007

Sample Output

328400734

p前面的第一个素数m与p的间隔大概在log p，m较大不能直接求m!，但我们可以通过威尔逊定理求得(p-1)!再除以m+1到p-1之间的数求得m!。

#include<cstdio>
#include<cmath>
#include<algorithm>
#include<string>
#include<cstring>
#include<map>
#include<queue>
#include<stack>
#include<set>
#include<vector>
#include<iostream>
#include<time.h>
using namespace std;
const int maxn=1e7+10;
const double exc=1e-7;
long long mod;
int cnt;
bool vis[maxn+10];
long long prime[maxn+10];
void getprime()
{for(int i=2; i<=maxn; i++){if(!vis[i])prime[cnt++]=i;for(int j=0; j<cnt&&i*prime[j]<=maxn; j++){vis[i*prime[j]]=1;if(i%prime[j]==0)break;}}
}
bool isprime(long long n)
{for(int i=0; i<cnt&&prime[i]*prime[i]<=n; i++){if(n%prime[i]==0){return false;}}return true;
}
long long fastmul(long long a,long long b)
{long long ans=0;while(b){if(b&1)ans=(ans+a)%mod;a=(a+a)%mod;b>>=1;}return ans%mod;
}
long long fastpow(long long a,long long b)
{long long ans=1;while(b){if(b&1)ans=fastmul(ans,a);a=fastmul(a,a);b>>=1;}return ans;
}
int main()
{int t;getprime();scanf("%d",&t);while(t--){long long p,m;scanf("%lld",&p);mod=p;m=p-1;while(!isprime(m)) m--; long long ans=p-1;for(long long i=p-1; i>=m+1; i--)ans=fastmul(ans,fastpow(i,p-2));printf("%lld\n",ans);}return 0;
}

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