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 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
const int N = 205;
const int maxS = 40005;
long long f[2][2*maxS],n,m,a[N];
const int MOD =1e9+7;
void init()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    freopen("AVERAGE.inp","r",stdin);
    freopen("AVERAGE.out","w",stdout);
}
void nhap()
{
    cin >> n >> m;
    for (int i=1; i<=n; i++) {
        cin >> a[i];
        a[i] -= m;
    }
}
void xuli()
{
    memset(f,0,sizeof(f));
    f[0][maxS] = 1;
    for (int i = 1; i<=n; i++) {
        for (int j = 0; j<2*maxS; j++) {
             f[1][j] += f[0][j];
             if (j+a[i]<2*maxS) f[1][j+a[i]] += f[0][j];
        }
        for (int j = 0; j<2*maxS; j++) {
            f[0][j] = f[1][j];
            f[1][j] = 0;
        }
    }
    cout << f[0][maxS] - 1  << '\n';
}
int main()
{
        nhap();
        xuli();

}