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(lambda x: int(x)-A, input().split()))
X_MAX = max(max(X), -min(X))
NX = N * X_MAX
dp = [[[0] * (N+1)  for i in range(N+1)] for _ in range(NX * 2 + 1)]
dp[NX][0][0] = 1
for i in range(1, N+1):
    for j in range(0, i+1):
        for k in range(NX * 2 + 1):
            if k == NX and j == 0:
                dp[k][i][j] = 1
                continue
            dp[k][i][j] += dp[k][i-1][j]
            if 0 <= k - X[i-1] < NX * 2 + 1:
                dp[k][i][j] += dp[k-X[i-1]][i-1][j-1]

print(sum(dp[NX][N]) - 1)