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>
#include <stdlib.h>
#include <cmath>
using namespace std;
typedef long long ll;

int N,A;
vector<ll> d;
ll dp[50][5001];

int i=0;

int main(){
    cin>>N>>A;
    for(int i=0;i<N;i++){
        ll x;
        cin>>x;
        x-=A;
        d.push_back(x);
    }

    dp[0][2500]++;
    dp[0][2500+d.at(0)]++;

    for(int i=1;i<N;i++){
        for(int j=0;j<5001;j++){
            dp[i][j]+=dp[i-1][j];
            if(0<=j-d.at(i) && j-d.at(i)<=5000) dp[i][j]+=dp[i-1][j-d.at(i)];
        }
    }

    cout<<dp[N-1][2500]-1<<endl;

    



}