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 solve():
    N,A = map(int,input().split())
    x = list(map(lambda a: int(a)-A,input().split()))

    GETA = 2500
    dp = [[0] * 5000 for _ in range(N+1)]
    dp[0][2500] = 1

    for i in range(N):
        for j in range(5000):
            if dp[i][j] == 0 or j+x[i] >= 5000:
                continue
            dp[i+1][j+x[i]] += dp[i][j]
            dp[i+1][j] += dp[i][j]
    
    print(dp[N][GETA]-1)
        
if __name__ == '__main__':
    solve()