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 ll = long long;
using namespace std;

int main() {
  cin.tie(0);
  cin.sync_with_stdio(0);

  int n, m;
  cin >> n >> m;
  vector<vector<ll>> dp(n + 1, vector<ll>(60 * 60));
  dp[0][0] = 1;
  for (int i = 0; i < n; ++i) {
    int x;
    cin >> x;
    int mx = 50 * 50 - x;
    for (int j = i; j >= 0; --j)
      for (int v = mx; v >= 0; --v) dp[j + 1][v + x] += dp[j][v];
  }

  ll ans = 0;
  for (int i = 1; i <= n; ++i) ans += dp[i][m * i];
  cout << ans;
}