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;
const int INF=55;
ll dp[INF][INF*INF]; 
int main(){
    int n,a;
    cin>>n>>a;
    int x;
    dp[0][0]=1;
    for(int i=0; i<n; i++){
        cin>>x;
        for(int j=i; j>=0; j--){
            for(int k=0; k<=INF*j; k++){   
                dp[j+1][k+x]+=dp[j][k];
            }
        }
    }
    ll ans=0;
    for(int i=1; i<=n; i++){
        ans+=dp[i][i*a];
    }
    cout<<ans<<endl;
    //system("pause");
    return 0;
}