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(v) for v in input().split() ]
num_list = [ int(v) for v in input().split() ]
max_num = max(num_list)
field = [ [ 0 for i in range(5000) ] for i in range(n+1) ]
field[0][0] = 1

b = num_list[0]
for i in num_list:
    for j in range(n,0,-1):
        for k in range(5000):
            if k >= i:
                field[j][k] += field[j-1][k-i]



ans = 0
for i in range(1,n+1):
    ans += field[i][a*i]
print(ans)