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)

'''
Created on 2016/08/28

@author: diyosko7
'''
import numpy
import itertools

if __name__ == '__main__':
    n = 2
    e = [[int(i) for i in input().split()] for i in range(n)] 
    l1 = e[0]
    l2 = e[1]
    N = l1[0]   #maisuu
    A = l1[1]   #heikin
    xList = l2  #x
    

    lst = []
    for i in range(0,N):
        lst.append(numpy.array(list(itertools.combinations(xList,i+1))))
    cnt = 0
    lst = numpy.array(lst)
    for l in lst:
        for s in l:
            if numpy.average(s) == A:
                cnt += 1
    print(cnt)