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)

// tsukasa_diary's programing contest code template
#include <bits/stdc++.h>
using namespace std;
#define TSUKASA_DIARY_S_TEMPLATE
// define
#define for_(i,a,b) for(int i=(a);i<(b);++i)
#define for_rev(i,a,b) for(int i=(a);i>=(b);--i)
#define allof(a) (a).begin(),(a).end()
#define minit(a,b) memset(a,b,sizeof(a))
#define size_of(a) int((a).size())
#define cauto const auto
// typedef
typedef long long lint;
typedef double Double;
typedef pair< int, int > pii;
template< typename T > using Vec = vector< T >;
template< typename T > using Matrix = Vec< Vec< T > >;
template< typename T > using USet = unordered_set< T >;
template< typename T, class C > using MyUSet = unordered_set< T, C >;
template< typename T, typename F > using UMap = unordered_map< T, F >;
template< typename T, typename F, class C > using MyUMap = unordered_map< T, F, C >;
// hash
class PiiHash { public: size_t operator () (const pii& p) const { return (p.first << 16) | p.second; } };
// popcount
inline int POPCNT(int x) { return __builtin_popcount(x); }
inline int POPCNT(lint x) { return __builtin_popcount(x); }
// inf
const int iINF = 1L << 30;
const lint lINF = 1LL << 60;
// eps
const Double EPS = 1e-9;
const Double PI = acos(-1);
// inrange
template< typename T >
inline bool in_range(T v, T mi, T mx) { return mi <= v && v < mx; }
template< typename T >
inline bool in_range(T x, T y, T W, T H) { return in_range(x,0,W) && in_range(y,0,H); }
// neighbor clockwise
const int DX[4] = {0,1,0,-1}, DY[4] = {-1,0,1,0};
const int DX_[8] = {0,1,1,1,0,-1,-1,-1}, DY_[8] = {-1,-1,0,1,1,1,0,-1};
// variable update
template< typename T > inline void modAdd(T& a, T b, T mod) { a = (a + b) % mod; }
template< typename T > inline void minUpdate(T& a, T b) { a = min(a, b); }
template< typename T > inline void maxUpdate(T& a, T b) { a = max(a, b); }
// converter
template< typename F, typename T >
inline void convert(F& from, T& to) {
	stringstream ss;
	ss << from; ss >> to;
}


int N, A, X[55];
map< int, lint > dp[55];

int main() {
	cin >> N >> A;
	
	for_(i,0,N) {
		cin >> X[i];
		X[i] -= A;
	}
	
	dp[0][0] = 1;
	
	for_(i,0,N) {
		for (pair< int, lint > p : dp[i]) {
			int j = p.first;
			lint c = p.second;
			
			dp[i + 1][j] += c;
			dp[i + 1][j + X[i]] += c;
		}
	}
	
	cout << dp[N][0] - 1 << endl;
}