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;

public class Main {
    static int N, A;
    static int[] x;
    static long[][][] dp;

    static long dfs(int idx, int sum, int cnt) {
        if (dp[idx][sum][cnt] != -1) {
            return dp[idx][sum][cnt];
        }
        if (idx == N) {
            if (cnt > 0 && sum % cnt == 0 && sum / cnt == A) {
                return 1;
            }
            return 0;
        }
        long res = 0;
        res += dfs(idx + 1, sum, cnt);
        res += dfs(idx + 1, sum + x[idx], cnt + 1);
        return dp[idx][sum][cnt] = res;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        while (sc.hasNextInt()) {
            N = sc.nextInt();
            A = sc.nextInt();
            x = new int[N];
            for (int i = 0; i < N; i++) {
                x[i] = sc.nextInt();
            }
            dp = new long[N + 1][N * 50 + 1][N + 1];
            for (int i = 0; i < N + 1; i++) {
                for (int j = 0; j < N * 50 + 1; j++) {
                    for (int k = 0; k < N + 1; k++) {
                        dp[i][j][k] = -1;
                    }
                }
            }
            System.out.println(dfs(0, 0, 0));
        }
    }
}