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 x[51];
ll dp[51][5001];
int main() {
  cin >> N >> A;
  int MAX = 0;
  for(int i = 0; i < N; i++) {
    cin >> x[i];
    MAX = max(MAX,x[i]);
    x[i] -= A;
  }


  dp[0][MAX * N] = 1;

  for(int i = 0; i < N; i++) {
    for(int k = 0; k < 2 * MAX * N; k++) {
      if(dp[i][k]) {
	dp[i+1][k+x[i]] += dp[i][k];
	dp[i+1][k] += dp[i][k];
      }
    }
  }

  cout << dp[N][MAX*N] - 1 <<endl;
}

  
