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<string>
#include<iostream>
#include<algorithm>
#include<set>
#include<math.h>
#include<vector>
#include<sstream>
#include<queue>
#include<functional>
#include<bitset>
#include<cstdio>
#include<iomanip>
#include<map>
#include<unordered_map>
#include<unordered_set>
#include <string.h>
using ll = long long;
 
#define rep(i, n) for(ll i = 0; i < (int)(n); i++)
#define reps(i,x) for(ll i=1;i<=(int)(x);i++)
#define rrep(i,x) for(ll i=((int)(x)-1);i>=0;i--)
#define rreps(i,x) for(ll i=(int)(x);i>0;i--)
#define all(x) (x).begin(),(x).end()
#define m0(x) memset(x,0,sizeof(x))
#define vll vector<ll>
#define vi vector<int>
#define mp make_pair
#define vpll vector<pair<ll,ll>>
#define vpi vector<pair<int,int>>
#define mod 1000000007 
using namespace std;
int x[50];
ll dp[51][51][2501];
int main() {
  int n, a;
  cin >> n >> a;
  reps(i,n)
    cin >> x[i];
  rep(i,n+1)
  dp[i][0][0] =1;
  reps(i,n)
     reps(j,n)
      rep(k,n*a+1){
        if(i > 0 && k < x[i]){
          dp[i][j][k] = dp[i-1][j][k];
	} else{
          dp[i][j][k] = dp[i-1][j][k]+dp[i-1][j-1][k - x[i]];
        }
      }
  ll ans = 0;
  reps(j,n)
	if(dp[n][j][j*a]) ans+=dp[n][j][j*a];
  cout << ans << endl;
  return 0;
}