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()))

dp = [list( [0 for _ in range(3000)] for _ in range(n+1)) for _ in range(n+1)]
dp[0][0][0] = 1


for i in range(n):
    for k in range(n):
        for s in range(sum(x)+1):
                dp[i+1][k][s] += dp[i][k][s]
                dp[i+1][k+1][s+x[i]] += dp[i][k][s]

ans = 0
for i in range(1,n+1):
    ans += dp[n][i][A*i]
print(ans)

