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, = map(int, input().split())
MAX = max(max(X), A) * N
X = [x - A for x in X]

dp = {i: {j: 0 for j in range(2*MAX+1)} for i in range(N+1)}
dp[0][MAX] = 1
for i in range(1, N+1):
    for j in range(2*MAX+1):
        t = j - X[i-1]
        dp[i][j] = dp[i-1][j] + (dp[i-1][t] if 0 <= t <= 2*MAX else 0)
print(dp[N][MAX]-1)