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;
typedef long long ll;

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    int n,a;
    cin >> n >> a;
    const int M=2500;
    vector<vector<ll>> dp(n+1,vector<ll>(M+1,0));
    dp[0][0]=1;
    for(int o=0;o<n;o++)
    {
        int x;
        cin >> x;
        for(int i=n-1;i>=0;i--)
        {
            for(int j=0;j+x<=M;j++) dp[i+1][j+x]+=dp[i][j];
        }
    }
    ll res=0;
    for(int i=1;i<=n;i++) res+=dp[i][a*i];
    cout << res << "\n";
    return 0;
}
