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())
l = [int(i) for i in input().split()]

dp = [[[0] * 2501 for j in range(51)] for i in range(51)]

dp[0][0][0] = 1

for i in range(n):
    for j in range(51):
        for k in range(2501):
            if k >= l[i] and j >= 1:
                dp[i+1][j][k] = dp[i][j][k] + dp[i][j-1][k-l[i]]
            else:
                dp[i+1][j][k] = dp[i][j][k]

print(sum([dp[n][m][a*m] for m in range(1, n+1)]))