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_x = max(x)
dp = [[0 for _  in range(n * 2 * max_x + 1)] for _ in range(n + 1)]

dp[0][n * max_x] = 1
for i in range(1, n + 1):
    for j in range(1, n * 2 * max_x + 1):
        if 0 <= j + a - x[i - 1] <= 2 * n * max_x:
            dp[i][j] = dp[i - 1][j] + dp[i - 1][j + a - x[i - 1]]
        else:
            dp[i][j] = dp[i - 1][j]

print(dp[n][n * max_x] - 1)