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,x[51];
long long ans,d[51][51][2501];
int main(){
	scanf("%d%d",&N,&A);
	for(int i=1;i<=N;i++)
		scanf("%d",x+i);
	d[0][0][0]=1;
	for(int i=1;i<=N;i++){
		for(int j=0;j<=N;j++){
			for(int k=0;k<=2500;k++){
				d[i][j][k]=d[i-1][j][k]+((k>=x[i] and j)?d[i-1][j-1][k-x[i]]:0);
			}
		}
	}
	for(int i=1;i<=N;i++)
		ans+=d[N][i][A*i];
	printf("%lld",ans);
	return 0;
}