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;
long long mat[52][3000]={0};

int main(){
	int n, a;cin>>n>>a;
	mat[0][0] = 1;
	for(int i=1; i<=n; i++){
		int temp;cin>>temp;
		for(int j=i; j>=0; j--){
			for(int k=0; k<=2500; k++)
			mat[j+1][k+temp]+=mat[j][k];
		}
	}
	long long ans = 0;
	for(int i=1; i<=n; i++)
		ans+=mat[i][i*a];
	cout<<ans<<endl;
	return 0;
}