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
f = lambda: list(map(int,input().split()))

n,a = f()
x = [int(x)-a for x in input().split()]
w = max(max(x),abs(min(x)),a)*n
dp = [[0 for _ in range(2*w + 1)] for _ in range(n+1)]
dp[0][w] = 1
for i in range(n):
    for j in range(2*w + 1):
        if 0 <= j-x[i] <= 2*w:
            dp[i+1][j] = dp[i][j-x[i]] + dp[i][j]
        else:
            dp[i+1][j] = dp[i][j]

print(dp[n][w]-1)