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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Data.List                                                                                                                                      
                                                                                                                                                      
main :: IO ()                                                                                                                                         
main = do                                                                                                                                             
  [n,a] <- map read . words <$> getLine :: IO [Int]                                                                                                   
  xs <- map read . words <$> getLine :: IO [Int]                                                                                                      
  print . length . filter (==Just a) . map average . subsequences $ xs                                                                                
                                                                                                                                                      
average :: [Int] -> Maybe Int                                                                                                                         
average [] = Nothing                                                                                                                                  
average xs = let s = sum xs                                                                                                                           
                 l = length xs                                                                                                                        
             in if s`mod`l==0                                                                                                                         
                then Just $ s`div`l                                                                                                                   
                else Nothing