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.*;

class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int A = sc.nextInt();
        int[] x = new int[N];
        for(int i=0;i<N;i++) x[i]=sc.nextInt();
        int sum=0;
        for(int w:x) sum+=w;
        long[][][] dp = new long[N+1][N+1][2501];
        dp[0][0][0]=1;
        for(int i=1;i<=N;i++){
            dp[i][0][0]=1;
            for(int j=1;j<=i;j++){
                dp[i][j][0]=0;
                for(int k=1;k<=sum;k++){
                    dp[i][j][k] += dp[i-1][j][k];
                    if(k>=x[i-1]) dp[i][j][k]+=dp[i-1][j-1][k-x[i-1]];
                }
            }
        }
        long ans = 0;
        for(int j=1;j<=N;j++){
            ans += dp[N][j][A*j];
        }
        System.out.println(ans);
    }
}