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 ll;
int N,A;
int a[51];
ll dp[51][51][2501];
int main() {
  cin >> N >> A;

  for(int i = 0; i <  N; i++) cin >> a[i];
  dp[0][0][0] = 1;

  for(int i = 0; i < N; i++) {
    for(int j = 0; j < N; j++) {
      for(int k = 0; k < 2501; k++) {
	if(dp[i][j][k]) {
	  dp[i+1][j][k] += dp[i][j][k];
	  dp[i+1][j+1][k+a[i]] += dp[i][j][k];
	}
      }
    }
  }
  ll ans = 0;

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