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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

n,a=map(int,input().split())
x=list(map(int,input().split()))

# n,a=4,8
# x=[7,9,8,9]
cnt=0
sum=0
ans=0
for i in range(2**n):
    sum=0
    Ave=0
    cnt=0
    for j in range(n):
        if j!=n-1:
            if i>>j&1:
                sum+=x[j]
                cnt+=1

        else:
            if i>>j&1:
                sum+=x[j]
                cnt+=1
                Ave=sum/cnt
                if a==Ave:
                    ans+=1
            elif cnt>=1:
                Ave=sum/cnt
                if a==Ave:
                    ans+=1



print(ans)