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
import sys
import copy

readline = sys.stdin.buffer.readline


def main():
    N, A = map(int, readline().split())
    X = list(map(int, readline().split()))
    X = [x - A for x in X]

    dp = [0] * 5050
    dp[2525] = 1

    for i in range(N):

        next_dp = copy.copy(dp)
        for t in range(5050):
            if X[i] + t < 5050:
                next_dp[X[i] + t] += dp[t]

        dp = next_dp

    print(dp[2525] - 1)


if __name__ == '__main__':
    main()
