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: Time Limit Exceeded)

import java.util.*;
import java.util.concurrent.atomic.AtomicInteger;
import java.util.function.Consumer;
import java.util.function.Function;
import java.util.stream.IntStream;

/**
 * Created by hirai on 2016/08/30.
 */
public class Main {

    private static long ans = 0;
    private static int expect_avg;
    private static int array_size;
    private static int[] array;

    public static final void main(String[] args) {
        final Scanner scanner = new Scanner(System.in);
        array_size = scanner.nextInt();
        expect_avg = scanner.nextInt();

        array = new int[array_size];
        for (int i = 0; i < array_size; i++) {
            array[i] = scanner.nextInt();
        }
        new Calc().accept(new Arg());

        System.out.println(ans);
    }

    /*
    private static void calc(int start, long sum, int cnt) {
        for (int i = start; i < array_size; i++) {
            final int tmp = array[i];
            final long avg = (sum + tmp) / (cnt + 1);
            final long remainder = (sum + tmp) % (cnt + 1);
            if (avg == expect_avg && remainder == 0) {
                ans++;
            }
            calc(i + 1, sum + tmp, cnt + 1);
        }
        //if(1==1)return 1;
        //else return calc(2,1,1);
    }
    */

    private static class Arg {
        int start = 0;
        long sum = 0;
        int cnt = 0;
    }

    private static class Calc implements Consumer<Arg> {

        @Override
        public void accept(Arg arg) {
            final int start = arg.start;
            final long sum = arg.sum;
            final int cnt = arg.cnt;
            for (int i = start; i < array_size; i++) {
                final int tmp = array[i];
                final long avg = (sum + tmp) / (arg.cnt + 1);
                final long remainder = (sum + tmp) % (cnt + 1);
                if (avg == expect_avg && remainder == 0) {
                    ans++;
                }
                Arg nextArg = new Arg();
                nextArg.start = i + 1;
                nextArg.sum = sum + tmp;
                nextArg.cnt = cnt + 1;
                new Calc().accept(nextArg);
            }
        }
    }
}