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()))
max_ = sum(x)

# dp[i枚目のカード][すでに何枚選んでいるか][値]
dp = [[[0] * (max_ + 1) for i in range(n + 1)] for i in range(n + 1)]
dp[0][0][0] = 1
for i in range(n):
    for j in range(n):
        for num in range(max_ + 1):
            # i枚目を選ぶ
            if num - x[i] >= 0:
                dp[i + 1][j + 1][num] += dp[i][j][num - x[i]]
            # i枚目を選ばない
            dp[i + 1][j][num] += dp[i][j][num]

ans = 0
for i in range(1, n + 1):
    for val in range(1, max_ + 1):
        if val == a * i:
            ans += dp[-1][i][val]
print(ans)
