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<iostream>
#include<cstring>
#include<queue>
#include<algorithm>
#include<cstdio>
using namespace std;
long long dp[60][60][2551];
int main(){
	dp[0][0][0]=1;
	int n,a,x[60],i,j,k;
	cin>>n>>a;
	for(i=0;i<n;i++) scanf("%lld",x+i);
	for(i=1;i<=n;i++){
		for(j=i;j>=0;j--){
			for(k=a*n+1;k>=0;k--){
				dp[i][j][k]+=dp[i-1][j][k];
                if(k>=x[i-1] && j>=1)
                    dp[i][j][k]+=dp[i-1][j-1][k-x[i-1]];
			}
		}
	}
	long long ans=0;
	for(int i=1;i<=n;i++) ans+=dp[n][i][a*i];
	printf("%lld",ans);
	return 0;
}