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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
using System.Linq;
using E = System.Linq.Enumerable;

class Program
{
    static void Main(string[] args)
    {   
        var NA = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var N = NA[0];
        var A = NA[1];
        var X = Console.ReadLine().Split().Select(int.Parse).ToArray();
        
        var dp = new long[N+1,N+1,A*N+1];
        
        for(int i = 0;i < N+1; i++){
          dp[i,0,0] = 1;
        }
   
        for(int i = 0;i < N; i++){
          for(int j = 1;j-1 <= i; j++){
            for(int k = 0;k < A*N+1; k++){
              dp[i+1,j,k] += dp[i,j,k];
              if(k >= X[i]){
                dp[i+1,j,k] += dp[i,j-1,k-X[i]];
              }
            }
          }
        }
      //Console.WriteLine(dp[3,1,8]);
        long ans = 0;
        for(int i = 1;i <= N;i++){
          ans += dp[N,i,A*i];
        }
        
        Console.WriteLine(ans);
      
    }

}