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: Runtime Error)

#include <bits/stdc++.h>

using namespace std ; 

int n , ar , a[ 52 ] ;
long long f[ 60 ][ 60 ][ 2510 ] ;
//选到i，选了j个，sum为k 

int main() {
	scanf( "%d%d" , &n , &ar ) ;
	for( int i = 1 ; i <= n ; i ++ ) {
		scanf( "%d" , &a[ i ] ) ;
	}
	
	f[ 0 ][ 0 ][ 0 ] = 1 ;
	
	for( int i = 1 ; i <= n ; i ++ ) {
		for( int j = i ; j >= 0 ; j -- ) {
			for( int k = ar * n + 1 ; k >= 0 ; k -- ) {
				f[ i ][ j ][ k ] += f[ i - 1 ][ j ][ k ] ; 
				if( k >= a[ i ] ) f[ i ][ j ][ k ] += f[ i - 1 ][ j - 1 ][ k - a[ i ] ] ;
			}
		}
	}
	long long ans = 0 ;
	for( int i = 1 ; i <= n ; i ++ ) {
		ans += f[ n ][ i ][ ar * i ] ;
	}
	printf( "%lld\n" , ans );
}