Problem:
Score : 300 points

Problem Statement

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.

Partial Score

200 points will be awarded for passing the test set satisfying 1 \leq N \leq 16.

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.

Sample Input 1

4 8
7 9 8 9

Sample Output 1

5

The following are the 5 ways to select cards such that the average is 8:

Select the 3-rd card.

Select the 1-st and 2-nd cards.

Select the 1-st and 4-th cards.

Select the 1-st, 2-nd and 3-rd cards.

Select the 1-st, 3-rd and 4-th cards.

Sample Input 2

3 8
6 6 9

Sample Output 2

0

Sample Input 3

8 5
3 6 2 8 7 6 5 9

Sample Output 3

19

Sample Input 4

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

Sample Output 4

8589934591

The answer may not fit into a 32-bit integer.

Solution in Julia (0.5.0) (judge verdict: Wrong Answer)

parseInt(x)=parse(Int,x)
d(x,a)=x%a==0?a:x%a
function main()
    n,a = map(parseInt,split(readline()))
    x = map(parseInt,split(readline()))
    z = zeros(Int,n,2500)
    count = 0
    ms = x[1]
    z[1,x[1]] += 1
    for i in 2:n
        z[i,x[i]] += 1
        for j in 1:ms
            z[i,j] += z[i-1,j]
            z[i,j+x[i]] += z[i-1,j]
        end
        ms += x[i]
    end
    k = 1
    while a*k<=2500
        count+=z[n,a*k]
        k+=1
    end
    println(count)
end
main()