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 HashMap<String,Long> h=new HashMap<String,Long>();
public static void main(String[] args)
{
 
Scanner sc=new Scanner(System.in);
int n=sc.nextInt();
double a=sc.nextDouble();
int ar[]=new int[n];
for(int i=0;i<n;i++)
ar[i]=sc.nextInt();
long pp=compute(0,ar,0,a,0);
System.out.println(pp);
}
    public static long compute(int index,int ar[],long sum,double a,int count)
{
    String zz=index+"|"+sum+"|"+count;
    if(h.containsKey(zz))
    return h.get(zz);
    else if(index==ar.length)
    {long zer=0;
        h.put(zz,zer);
    return zer;
    }
    else{
    long uu=sum+ar[index];
    double kk=1.0*uu;
    double ff=kk/(count+1);
    long counter=(ff==a)?1:0;
    
    counter+=compute(index+1,ar,uu,a,count+1);
    counter+=compute(index+1,ar,sum,a,count);
    h.put(zz,counter);
    return  counter;
    }
}}