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;
#define rep(i, m, n) for (int i = m; i < n; ++i)

int main() {
    int N, A;
    cin >> N >> A;
    vector<int> x(N);
    rep(i, 0, N) cin >> x[i], x[i] -= A;
    vector<vector<long long>> dp(N + 1, vector<long long>(5555));
    int g = 2500;
    dp[0][g] = 1;
    rep(i, 0, N) rep(j, -g, g) {
        dp[i + 1][j + g] += dp[i][j + g];
        dp[i + 1][j + g + x[i]] += dp[i][j + g];
    }
    cout << dp[N][g] - 1 << endl;
    return 0;
}
