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 = (int(i) for i in input().split())
x = [int(i) for i in input().split()]
sumx = sum(x)
DP = [[[0] * (N+1) for i in range(sumx+1)] for i in range(N+1)]
DP[0][0][0] = 1
for i in range(N):
    for j in range(sumx+1):
        for k in range(i+1):
            if j - x[i] >= 0:
                DP[i+1][j][k+1] += DP[i][j-x[i]][k]
            DP[i+1][j][k] += DP[i][j][k]

res = 0
for i in range(1,N+1):
    if i * A <= sumx:
        res += DP[N][i * A][i]
print(res)