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
N,A = map(int,input().split())
x = list(map(int,input().split()))
X = N*50
dp = [[[0 for i in range(X+1)] for j in range(N+1)] for k in range(N+1)]
dp[0][0][0] = 1
for k in range(1,N+1):
    for j in range(k+1):
        for i in range(j*50+1):
            if i - x[k-1] < 0:
                dp[k][j][i] = dp[k-1][j][i]
            elif k >= 1:
                dp[k][j][i] = dp[k-1][j-1][i-x[k-1]] + dp[k-1][j][i]
ans = 0
for j in range(1,N+1):
    ans += dp[-1][j][j*A]
print(ans)