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
# ABC044C - 高橋君とカード / Tak and Cards (ARC060C)
def main():
    N, A = tuple(map(int, input().split()))
    X = tuple(map(int, input().split()))
    # dp[i][j][k] := patterns to make k with j cards from X1, X2, ..., Xi
    dp = [[[0] * (N * 50 + 1) for _ in range(N + 1)] for _ in range(N + 1)]
    dp[0][0][0] = 1
    for i in range(N):
        for j in range(N):
            for k in range(N * 50 + 1):
                if dp[i][j][k]:
                    dp[i + 1][j][k] += dp[i][j][k]
                    dp[i + 1][j + 1][k + X[i]] += dp[i][j][k]
    ans = sum(dp[N][i][i * A] for i in range(1, N + 1))
    print(ans)


if __name__ == "__main__":
    main()
