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 int64;

int main()
{
  int64 dp[51][2501] = {{}};
  int N, A, X[50];

  cin >> N >> A;
  for(int i = 0; i < N; i++) cin >> X[i];
  dp[0][0] = 1;
  for(int i = 0; i < N; i++) {
    for(int j = 49; j >= 0; j--) {
      for(int k = 2500; k >= X[i]; k--) {
        dp[j + 1][k] += dp[j][k - X[i]];
      }
    }
  }


  int64 ret = 0;
  for(int i = 1; i <= N; i++) {
    ret += dp[i][A * i];
  }
  cout << ret << endl;
}