Tak has N cards. On the i-th (1 \leq i \leq N) card is written an integer x_i. He is selecting one or more cards from these N cards, so that the average of the integers written on the selected cards is exactly A. In how many ways can he make his selection?

Constraints

* 1 \leq N \leq 50
* 1 \leq A \leq 50
* 1 \leq x_i \leq 50
* N,\,A,\,x_i are integers.

Input

The input is given from Standard Input in the following format:


N A
x_1 x_2 ... x_N


Output

Print the number of ways to select cards such that the average of the written integers is exactly A.

Examples

Input

4 8
7 9 8 9


Output

5


Input

3 8
6 6 9


Output

0


Input

8 5
3 6 2 8 7 6 5 9


Output

19


Input

33 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3


Output

8589934591
#include<bits/stdc++.h>
using namespace std;
int n,a,num[112];
long long knap[55][2510];
long long totalsum = 0;

int main()
{
	int i,j,k;
	
	scanf("%d %d",&n,&a);
	for(i=0;i<n;i++)
	{
		scanf("%d",&num[i]);
	}
	
	knap[0][0] = 1;
	for(i=0;i<n;i++)
	{
		for(j=n-1;j>=0;j--)
		{
			for(k=0;k<=2500;k++)
			{
				knap[j+1][k+num[i]] += knap[j][k];
			}
		}
	}
	
	int mul=0;
	for(i=1;i<=n;i++)
	{
		mul += a;
		totalsum += knap[i][mul];
	}
	printf("%lld\n",totalsum);
	
}