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;
#define int long long
const int N=55;
int n,A,a[N],ans,dp[N][N][N*N];
signed main(){
	scanf("%lld%lld",&n,&A);
	for (int i=1;i<=n;i++)scanf("%lld",&a[i]);
	dp[0][0][0]=1;
	for (int i=1;i<=n;i++)
		for (int j=0;j<=n;j++)
			for (int k=0;k<=n*50;k++){
				dp[i][j][k]+=dp[i-1][j][k];
				if (j&&k>=a[i])dp[i][j][k]+=dp[i-1][j-1][k-a[i]];
			}
	for (int i=1;i<=n;i++)ans+=dp[n][i][i*A];
	printf("%lld\n",ans);
}