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 <cstdio>
#include <iostream>
using namespace std;
#define REP(i, n) for(int i = 0; i < (int)(n); ++i)
typedef long long ll;

ll dp[60][2600];

int main(void) {
  int n;
  int avg;
  scanf("%d%d", &n, &avg);

  dp[0][0] = 1;
  REP(i, n) {
    int v;
    scanf("%d", &v);
    for(int j = i; j >= 0; --j) {
      for(int k = 2500; k >= 0; --k) {
        dp[j+1][k+v] += dp[j][k];
      }
    }
  }

  ll res = 0;
  for(int i = 1; i <= n; ++i) {
    res += dp[i][i*avg];
  }
  printf("%lld\n", res);
  
  return 0;
}
