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;

long long dp[52][2600];
int main() {
    int n, a;
    cin >> n >> a;
    dp[0][0] = 1;
    for (int i = 0; i < n; ++i) {
        int x;
        cin >> x;
        for (int j = i; j >= 0; --j) {
            for (int k = 2550; k >= x; --k) {
                dp[j + 1][k] += dp[j][k - x];
            }
        }
    }
    long long ans = 0;
    for (int i = 1; i <= n; ++i) {
        ans += dp[i][i * a];
    }
    cout << ans << "\n";
    return 0;
}
