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 <iostream>

using namespace std;

const int N = 55;

int x[N];
long long f[N][N * N];

int main() {
  int n, A;
  cin >> n >> A;
  for (int i = 1; i <= n; ++i) {
    cin >> x[i];
  }
  f[0][0] = 1;
  for (int i = 1; i <= n; ++i) {
    for (int j = i - 1; j >= 0; --j) {
      for (int k = N * N - 1; k >= 0; --k) {
        if (k >= x[i]) {
          f[j + 1][k] += f[j][k - x[i]];
        }
      }
    }
  }
  long long ans = 0;
  for (int i = 1; i <= n; ++i) {
    ans += f[i][A * i];
  }
  cout << ans << endl;
  return 0;
}