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[55];
long long dp[55][55][2555];
int main()
{
    scanf("%d%d",&n,&a);
    for (int i=1;i<=n;++i) scanf("%d",&x[i]);
    dp[0][0][0]=1;
    for (int i=1;i<=n;++i) {
        for (int j=0;j<=i;++j)
            for (int k=0;k<=2500;++k) {
            dp[i][j][k]+=dp[i-1][j][k];
            dp[i][j+1][k+x[i]]+=dp[i-1][j][k];
        }
    }
    long long res=0;
    for (int i=1;i<=n;++i)
        res+=dp[n][i][i*a];
    cout<<res<<endl;
    return 0;
}
