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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

n,a=map(int,input().split())
x=list(map(int,input().split()))
t=[[[0 for s in range((n+1)*a+1)]for k in range(n+1)]for j in range(n+1)]
ans=0
for j in range(n+1):
  for k in range(n+1):
    if k>j:
      break
    for s in range((n+1)*a+1):
      if s==0 and k==0 and j==0:
        t[j][k][s]=1
      elif j>=1 and x[j-1]>s:
        t[j][k][s]=t[j-1][k][s]
      elif j>=1 and k>=1 and x[j-1]<=s:
        t[j][k][s]=t[j-1][k][s]+t[j-1][k-1][s-x[j-1]]
      if j==n and k>=1 and s==k*a:
        ans+=t[j][k][s]
print(ans)