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;

long long dp[51][51][2501] = {0};

int main(){
  long long n,a;
  cin >> n >> a;
  int x[n+1];
  for(int i = 1;i <= n;i++)
    cin >> x[i];
  dp[0][0][0] = 1;
  for(int i = 1; i < n+1;i++){
    for(int j = 0;j < n+1;j++){
      for(int k = 0; k < 2501;k++){
	dp[i][j][k] = dp[i-1][j][k];
	if(j > 0 && k >= x[i])
	  dp[i][j][k] += dp[i-1][j-1][k-x[i]];
      }
    }

  }

  long long res = 0;
  for(int i = 1;i<n+1;i++){
    res += dp[n][i][i*a];
  }

  cout << res << endl;

}
