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;

int main()
{
    int N, A;
    int X[55];
    ll dp[55][5500] = {};

    cin >> N >> A;

    dp[0][2600] = 1;

    for(int i = 0; i < N; i++) {
        cin >> X[i]; X[i] -= A;
    }

    for(int i = 0; i < N; i++) {
        for(int j = 0; j <= 5400; j++) {
            dp[i + 1][j + X[i]] += dp[i][j];
            dp[i + 1][j] += dp[i][j];
        }
    }

    cout << dp[N][2600] - 1 << endl;


    return (0);
}
