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():
    offset = 2500
    W = 2 * offset + 1
    N, A = list(map(int, input().split(' ')))
    x = list(map(int, input().split(' ')))
    y = [xx - A for xx in x]
    dp = [[0 for _ in range(W)] for _ in range(N)]
    dp[0][0 + offset] += 1
    dp[0][y[0] + offset] += 1
    for i in range(1, N):
        for j in range(W):
            dp[i][j] = dp[i - 1][j]
            if 0 <= j - y[i] <= W - 1:
                dp[i][j] += dp[i - 1][j - y[i]]
    print(dp[N - 1][0 + offset] - 1)  # remove the no card case


if __name__ == '__main__':
    main()
