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 <stdio.h>

int x[55];
long long dp[55][2555];

int main(){
    int N, A;
    scanf("%d%d", &N, &A);
    dp[0][0] = 1;
    for(int i=0; i<N; i++){
        scanf("%d", &x[i]);
        for(int j=54; j>=1; j--){
            for(int k=2555; k>=x[i]; k--){
                dp[j][k] += dp[j-1][k-x[i]];
            }
        }
    }
    long long res=0;
    for(int i=1; i<=N; i++) res += dp[i][i*A];
    printf("%lld", res);
    return 0;
}