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(lambda x: int(x) - A, input().split()))
    D = {0: 1}
    for i in X:
        for j, k in list(D.items()):
            D[i + j] = D.get(i + j, 0) + k
    ans = D[0] - 1
    print(ans)


if __name__ == "__main__":
    main()