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
def main():
    n, a = list(map(int, input().split()))
    X = list(map(lambda x: int(x) - a, input().split()))
    b = max(max([x for x in X]) + a, a)
    dp = [[0] * (2 * b * n + 1) for  _ in range(n + 1)]
    dp[0][b * n] = 1
    for i in range(1, n + 1):
        for j in range(2 * b * n + 1):
            if 0 <= j - X[i - 1] < 2 * b * n:
                dp[i][j] = dp[i - 1][j] + dp[i - 1][j - X[i - 1]]
            else:
                dp[i][j] = dp[i - 1][j]
    print(dp[n][b * n] - 1)

if __name__ == '__main__':
    main()
