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 = list(map(int, input().split()))
xs = list(map(int, input().split()))

na = n*a

DP = [[0]*(na+1) for i in range(n+1)]
DP[0][0] = 1

for _ in range(n):
    x = xs[_]
    next = [[0]*(na+1) for i in range(n+1)]
    for i in range(_+1):
        for j in range(na+1):
            # xを使わないとき
            next[i][j] += DP[i][j]
            if j+x <= na:
                next[i+1][j+x] += DP[i][j]
    DP = next

# i枚使ったとき合計がi*aである場合の数
ans = 0
for i in range(1,n+1):
    ans += DP[i][i*a]
print(ans)