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)

I = lambda: map(int, input().split())
N, A = I()
x = list(I())

from collections import deque
import copy
memo = []
checked = []
q = deque()
q.append([False]*N)

while q:
    indexs = q.popleft()
    if indexs in checked:
        continue
    checked.append(indexs)
    sum_x = 0
    for i, bit in enumerate(indexs):
        if bit:
            sum_x += x[i]

    if indexs.count(True) > 0 and sum_x / indexs.count(True) - A == 0:
        if indexs not in memo:
            memo.append(indexs)

    for i in range(N):
        a = copy.deepcopy(indexs)
        a[i] = not(a[i])
        if a not in checked:
            q.append(a)

print(len(memo))