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 _ in range(3000)] for _ in range(N + 1)] for _ in range(N + 1)]
dp[0][0][0] = 1

for i in range(N):
    for j in range(N):
        for t in range(2501):
            dp[i + 1][j][t] += dp[i][j][t]
            dp[i + 1][j + 1][t + X[i]] += dp[i][j][t]

ans = 0

for i in range(1, N + 1):
    ans += dp[N][i][i * A]

print(ans)
