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>
#include <algorithm>
#include <string>
#include <vector>
using namespace std;

#define int long long
int N, A;
int D[51][2501];

signed main() {
  cin >> N >> A;
  D[0][0] = 1;
  for (int i=0; i<N; i++) {
    int x;
    cin >> x;
    for (int j=i; j>=0; j--) {
      for (int k=0; k<=50*(j+1); k++) {
        D[j+1][k+x] += D[j][k];
      }
    }
  }
  int c = 0;
  for (int i=1; i<=N; i++) {
    c += D[i][i*A];
  }
  cout << c << "\n";
  return 0;
}
