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: Runtime Error)

import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Main {


	static int ave;
	static long[][] memo;
	
    public static void main(String[] args) {
    	
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        ave = in.nextInt();
        long ans = 0;
        memo = new long[n][2000];
        
        int[] num = new int[n];
        
        for(int i=0;i<n;i++){
        	num[i]=in.nextInt();
        }
        
        ans = card_ave(num,0,0,0);
        
        System.out.println(ans);


        in.close();
    }

	private static long card_ave(int[] num, int i, int weight,int objective) {
		// TODO 自動生成されたメソッド・スタブ
		
		long ans = 0;
//		if(weight != 0) ans = weight==objective?1:0;
		
				
		if(i == num.length) return ans;
		if(memo[i][weight-objective+1000]!=0) return memo[i][weight-objective+1000]; 
		
		ans += card_ave(num , i+1,weight + num[i], objective+ave); 
		ans += weight+num[i]==objective+ave?1:0;
		ans += card_ave(num , i+1,weight, objective);
		
		memo[i][weight-objective+1000] = ans;
		
		return ans;
	}
}