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>

using namespace std;
typedef long long ll;
typedef double dd;
#define all(v) v.begin(),v.end()
#define endl "\n";

void fast() {

    cin.tie(0);
    cin.sync_with_stdio(0);
}
ll n,a,arr[50+9],dp[50+9][50+9][2550];
ll ans(int i,int num,int sum){
    ll &ret=dp[i][num][sum];
    if(~ret)return ret;
    if(i==n)return dp[i][num][sum]=num&&((dd)sum/(dd)num==a);


    return ret=ans(i+1,num,sum)+ans(i+1,num+1,sum+arr[i]);

}
int main() {
        fast();
        cin>>n>>a;
    for (int i = 0; i <n ; ++i) {
        cin>>arr[i];
    }
    memset(dp,-1, sizeof(dp));
    cout<<ans(0,0,0);
}