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 = [[[0 for k in range(50 * N + 1)] for j in range(N + 1)] for i in range(N + 1)]

for i in range(N):
    dp[i][0][0] = 1

for i in range(N):
    for j in range(N):
        for k in range(50 * N + 1):
            if k - X[i] >= 0:
                dp[i + 1][j + 1][k] += dp[i][j][k - X[i]]
            dp[i + 1][j + 1][k] += dp[i][j + 1][k]

res = 0

for j in range(N + 1):
    for k in range(50 * N + 1):
        if k == j * A:
            res += dp[N][j][k]

print(res)