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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

class Program {
	static void Main(string[] args){
		int M = 52;
		int N = 2503;
		long[,,] tb = new long[M,M,N];
		for(int i=0;i<M;i++){
			for(int j=0;j<M;j++){
				for(int k=0;k<N;k++){
					tb[i,j,k] = 0;
				}
			}
		}
		string[] str = Console.ReadLine().Split(' ');
		int  n = int.Parse(str[0]);
		long  a = long.Parse(str[1]);
		long[] x = new long[n];
		str = Console.ReadLine().Split(' ');
		for(int i=0;i<n;i++){
			x[i] = long.Parse(str[i]);
		}
		
		long ans = 0;
		for(int j=0;j<n+1;j++){
			for(int k=0;k<N;k++){
				tb[0,j,k] = 0;
			}
		}
		tb[0,0,0] = 1;
		for(int i=1;i<n+1;i++){
			for(int j=0;j<n+1;j++){
				for(int k=0;k<N;k++){
					tb[i,j,k] = tb[i-1,j,k];
					if(k-x[i-1]>=0 && j>0) tb[i,j,k] += tb[i-1,j-1,k-x[i-1]];
				}
			}
		}
		for(int i=1;i<n+1;i++) ans += tb[n,i,i*a];
		Console.WriteLine(ans);
	}
}