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;
LL dp[55][5005];
int main(){
    int n, a, x;
    scanf("%d%d", &n, &a);
    dp[0][2500] = 1;
    for(int i=1;i<=n;i++){
        scanf("%d", &x);
        for(int j=0;j<=5000;j++) dp[i][j+x-a] += dp[i-1][j], dp[i][j] += dp[i-1][j];
    }
    printf("%lld\n", dp[n][2500]-1);
}