Here you will find solutions of many problems on spoj. If you want solution of some problem which is not listed in blog or have doubt regarding any spoj problem (which i have solved) or any programming concept (data structure) you can mail me @ raj.nishant360@gmail.com
And my humble request to you all that don't copy the code only try to understand the logic and algorithm behind the code. I have started this because if you tried as hard as you can and still can't find any solution to the problem then you can refer to this.

## Thursday, May 22, 2014

### Boring Factorials

given below code for dcepc11b spoj or boring factorial spoj.
here the problem is based on two main concepts
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

According to Wilson's Theorem    $(n-1)!\ \equiv\ -1 \pmod n$ 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;
}