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: Wrong Answer)

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

dp=[[[0]*(sum(X)+1) for _ in range(n+1)] for _ in range(n+1)]

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

for i in range(1,n+1): #x_1,x_2...x_n
  for k in range(i):   #k枚数選ぶ
    for s in range(sum(X)+1): #合計
      if dp[i-1][k][s]:
        dp[i][k+1][s+X[i-1]]+=dp[i-1][k][s] #1枚選択肢が増えた時の、そのカードを加えた結果を加算
        dp[i][k][s]+=dp[i-1][k][s]
ans=0
for i in range(1,n):
  for j in range(1,sum(X)+1):
    if j == i*a: #合計が平均のi倍の時に加える
      ans+=dp[n][i][j]

print(ans)