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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;
import java.util.List;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Set;
import java.util.Map;
import java.util.HashMap;

public class Main {
    public static void main(String[] args) throws Exception {
        // Here your code !
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int A = sc.nextInt();
        int NA = N*A;
        int[] x = new int[N];
        int[] sumfx = new int[N];
        int sumx = 0;
        for(int i=0;i<N;i++){
            x[i] = sc.nextInt();
        }
        
        long[][][] p = new long[N+1][N+1][2501];
        p[0][0][0] = 1;
        
        for(int i=1;i<=N;i++){
            for(int j=0;j<=N;j++){
                for(int s=0;s<=2500;s++){
                    if(j>0&&(s-x[i-1])>=0){
                        p[i][j][s] = p[i-1][j][s] + p[i-1][j-1][s-x[i-1]];
                    }else{
                        p[i][j][s] = p[i-1][j][s];
                    }
                }
            }
        }
        
        long result = 0;
        for(int k=1;k<=N;k++){
            result += p[N][k][k*A];
        }
        
        System.out.println(result);
        
    }
}