Balls in the Boxes

Description

Mr. Mindless has many balls and many boxes,he wants to put all the balls into some of the boxes.Now, he wants to know how many different solutions he can have.

you know,he could put all the balls in one box,and there could be no balls in some of the boxes.Now,he tells you the number of balls and the numbers of boxes, can you to tell him the number of different solutions? Because the number is so large, you can just tell him the solutions mod by a given number C.

Both of boxes and balls are all different.

Input

There are multiple testcases. In each test case, there is one line cantains three integers:the number of boxes ,the number of balls,and the given number C separated by a single space.All the numbers in the input are bigger than 0 and less than 2^63.

Output

 For each testcase,output an integer,denotes the number you will tell Mr. Mindless

Sample Input

3 2 4
4 3 5

Sample Output

1
4

Hint

#include<cstdio>
#include<iostream>
using namespace std;
typedef unsigned long long ull;
unsigned long long fast_mod(ull a,ull b,ull mod)
{
    ull res=0;
    while(b)
	{
        if(b&1) res=(res+a)%mod;
        a=(2*a)%mod;
        b>>=1;    
    }
    return res;
}

unsigned long long work(ull a,ull b,ull mod)
{
    ull res=1;
    while(b)
	{
        if(b&1)
            res=fast_mod(res,a,mod);
        a=fast_mod(a,a,mod);
        b>>=1;
    }
    return res;
}

int main()
{
    ios::sync_with_stdio(false);
    ull a,b,c;
    while(cin>>a>>b>>c)
	{
        cout<<work(a,b,c)<<endl;
    }
    return 0;
}
/**********************************************************************
	Problem: 1162
	User: song_hai_lei
	Language: C++
	Result: AC
	Time:60 ms
	Memory:2180 kb
**********************************************************************/