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 "IntMod.h"
//typedef IntMod<1000000007> MInt;

//#include "Union_Find.h"

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <string>
#include <vector>
#include <utility>
#include <algorithm>
#include <functional>
#include <cmath>
#include <stack>
#include <queue>
#include <set>
#include <map>
//#include <unordered_set>
//#include <unordered_map>
#include <iomanip>
#include <sstream>

using namespace std;
#define REP(i,a,n) for(int i = a; i < n; ++i)
#define REPM(i,n,a) for(int i = n - 1; i >= a; --i)
#define EPS 0.0001
#define INF 0x3FFFFFFF
#define INFLL 0x3FFFFFFF3FFFFFFF
#define INFD 1.0e+308
typedef long long LL;
typedef unsigned long long ULL;

class SplitStream {
	typedef basic_ostream<char, char_traits<char> > BaseOst;
	std::ostream& ost_m;
	bool line_is_empty_m;
public:
	SplitStream(std::ostream& ost);
	template <typename T>
	SplitStream& operator<<(T right);
	SplitStream& operator<<(BaseOst& (*right)(BaseOst&));
};
SplitStream::SplitStream(std::ostream& ost) : ost_m(ost), line_is_empty_m(true) {}
template <typename T>
SplitStream& SplitStream::operator<<(T right) {
	if (!line_is_empty_m) ost_m << ' ';
	line_is_empty_m = false;
	ost_m << right;
	return *this;
}
/* std::endl のみ */
SplitStream& SplitStream::operator<<(BaseOst& (*right)(BaseOst&)) {
	ost_m << '\n';
	ost_m.flush();
	line_is_empty_m = true;
	return *this;
}
SplitStream Scout(cout);

template <typename T, int Begin, int End>
class OffsetArray {
	T arr_m[End - Begin];
public:
	OffsetArray();

	T& operator[](int index);
	T operator[](int index) const;
};
template<typename T, int Begin, int End>
OffsetArray<T, Begin, End>::OffsetArray() : arr_m() {}

template<typename T, int Begin, int End>
T & OffsetArray<T, Begin, End>::operator[](int index) {
	return arr_m[index - Begin];
}

template<typename T, int Begin, int End>
T OffsetArray<T, Begin, End>::operator[](int index) const {
	return arr_m[index - Begin];
}


LL N, A, X[50];
OffsetArray<LL, -2501, 2501> DP[51];

int main() {
	cin >> N >> A;
	REP(i, 0, N) {
		cin >> X[i];
		X[i] -= A;
	}
	DP[0][0] = 1;
	REP(i, 0, N) {
		REP(j, -N * 50, N * 50) {
			DP[i + 1][j] = DP[i][j] + DP[i][j - X[i]];
		}
	}
	cout << DP[N][0] - 1 << endl;
	return 0;
}