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;

long long n, a, x[55], dp[55][55][2525];
long long sum=0;


int main(){

cin >> n >> a;
for(int i =0; i<n;i++)cin >> x[i];
dp[0][0][0]=1;
for(int i =0; i<=50; i++){
    for(int j =0; j<=50; j++){
        for(int k =0; k<=2505; k++){
            if(dp[i][j][k]){
                dp[i+1][j+1][k+x[i]] += dp[i][j][k];
                dp[i+1][j][k] += dp[i][j][k];
            }
        }
    }
}
for(int i =1; i<=n; i++){
    sum+= dp[n][i][a*i];
}
cout << sum << endl;
return 0;}
