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<cstdio>
typedef long long ll;
using namespace std;

int a[55];
int sum[55];
ll dp[55][2505];

int main()
{
    int n,A;
    scanf("%d%d",&n,&A);
    for(int i=1;i<=n;i++) 
	{
	scanf("%d",&a[i]); sum[i]=sum[i-1]+a[i];
	}
    dp[0][0]=1;
    for(int k=1;k<=n;k++){
        for(int i=k;i>=1;i--){
            for(int j=a[k];j<=sum[k];j++){
                dp[i][j]+=dp[i-1][j-a[k]];
            }
        }
    }
    ll ans=0;
    for(int i=1;i<=n;i++) ans+=dp[i][i*A];
    printf("%lld\n",ans);
    return 0;
}