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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h> 
using namespace std;
typedef long long LL;
typedef double DB;

#define F(i,a,b) for(int i=(a);i<=(b);++i)
#define R(i,n) for(int i=0;i<(n);++i)
#define fill(a,b) memset(a,b,sizeof(a))

LL d[55][3000];
int n,A;

int main()
{
	//freopen("test.txt","r",stdin);
	scanf("%d %d",&n,&A);
	d[0][0] = 1;
	F(i,1,n)
	{
		int x;
		scanf("%d",&x);
		for(int j=i;j>0;--j)
		{
			for(int k=n*A;k-x>=0;--k)
			{
				d[j][k] += d[j-1][k-x];
			}
		}
	}
	LL ans = 0;
	F(i,1,n) ans += d[i][i*A];
	printf("%lld\n",ans);
	return 0;
}