DCEPC11B-Boring Factorials

Boring Factorials

given below code for dcepc11b spoj or boring factorial spoj.

here the problem is based on two main concepts 

1 -> Wilson’s Theorem 

2 -> Inverse modulo (It can be found by Extended Euclidean Algorithm , Fermat’s Little Theorem ,Euler’s Theorem)

here in this problem i have used Fermat's theorem 

Wilson’s Theorem 

According to Wilson's Theorem     for all prime n;(for proof of Wilson's Theorem click on link)

Now from this we can write :

Here my solution get accepted in 1.83 sec can any body help me in optimizing this solution or any other solution which get accepted in lower time please mail me @ raj.nishant360@gmail.com

#include <bits/stdc++.h>
using namespace std;
#define LL long long
LL pow_mod(LL a,LL b,LL m)
{
 LL x=1,y=a;
 while(b>0)
 {
  if(b & 1)
   x=(x*y)%m;
  y=(y*y)%m;
  b>>=1;
 }
 return x;
}
int main()
{
 int t;
 scanf("%d",&t);
 while(t--)
 {
  LL n,p,i,result=-1,temp;
  scanf("%lld%lld",&n,&p);
  if(n>=p)
  {
   printf("0\n");
   continue;
  }
  for(i=n+1;i<p;i++)
  {
   temp=pow_mod(i,p-2,p);
   result=(result*temp)%p;
  }
  printf("%lld\n",p+result);
 }
 return 0;
}