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;
int N, A, x[50];
long long dp[52][3001];
int main()
{
    scanf("%d%d", &N, &A);
    for(int i=0; i<N; ++i) scanf("%d", x+i);
    dp[0][0] = 1;
    for(int k=0; k<N; ++k)
        for(int i=k; i>=0; --i)
            for(int j=0; j<=50*i; ++j)
                dp[i+1][j+x[k]] += dp[i][j];
    long long ans = 0;
    for(int i=1; i<=N; ++i)
        ans += dp[i][A*i];
    printf("%lld\n", ans);
    return 0;
}