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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define ll long long
using namespace std;
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    ll n,a;
    cin>>n>>a;
    ll b[60];
    for(int i=1;i<=n;i++)
    {
        cin>>b[i];
    }
    ll dp[5000][5000];
    memset(dp,0,sizeof(dp));
    dp[0][0]=1;
    for(int i=1;i<=n;i++)
    {
        for(int j=i-1;j>=0;j--)
        {
            for(int k=0;k<=2500;k++)
            {
                dp[j+1][k+b[i]]+=dp[j][k];
            }
        }
    }
    ll ans=0;
    for(int i=1;i<=n;i++)
    {
        ans+=dp[i][a*i];
    }
    cout<<ans;
    return 0;
}