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>

int const SH = 50 * 100 + 2;

long long dp[2 * SH];

int main() {
  int n, A;
  scanf("%d%d", &n, &A);
  dp[SH] = 1;
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%d", &x);
    x -= A;
    if (x == 0) {
      for (int j = 0; j < 2 * SH; j++) dp[j] *= 2;
    } else if (x < 0) {
      for (int j = 0; j < 2 * SH; j++) dp[j] += dp[j - x];
    } else {
      for (int j = 2 * SH - 1; j >= 0; j--) {
        dp[j] += dp[j - x];
      }
    }
  }
  printf("%lld\n", dp[SH] - 1);
}