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.*;

public class Main{
    static int N;
    static int A;
    static int[] x;
    static long count;
    static int sum;
    static int max;
    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);

        N = sc.nextInt();
        A = sc.nextInt();
        x = new int[N];
        max = A;
        for(int i = 0;i < N; i++){
            x[i] = sc.nextInt();
            max = Math.max(max, x[i]);
            x[i] -= A;
        }
        sc.close();
        long[][] dp = new long[N+1][2*N*max+1];
        for(int i = 0; i < N+1; i++){
            for(int j = 0; j < dp[i].length; j++){
                if(i == 0){
                    if(j == N*max)
                        dp[i][j] = 1;
                    else
                        dp[i][j] = 0;
                } else {
                    if(j-x[i-1] < 0 || j-x[i-1] > 2*N*max)
                        dp[i][j] = dp[i-1][j];
                    else
                        dp[i][j] = dp[i-1][j] + dp[i-1][j-x[i-1]];
                }
            }
        }
        System.out.println(dp[N][N*max]-1);
    }
}