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 makelist(n,m,p):
    return [[[0 for k in range(p)]for i in range(m)]for j in range(n)]

n,a = map(int,input().split())
x = list(map(int,input().split()))
X = max(x)
X = max(X,a)

dp = makelist(n+1,n+1,n*X+1)
dp[0][0][0] = 1
for j in range(n+1):
    for k in range(n+1):
        for s in range(n*X+1):
            if j*k > 0 and s >= x[j-1]:
                dp[j][k][s] = dp[j-1][k][s] + dp[j-1][k-1][s-x[j-1]]
            elif j >= 1 and s < x[j-1]:
                dp[j][k][s] = dp[j-1][k][s]
ans = 0
for k in range(1,n+1):
    ans += dp[n][k][k*a]
print(ans)