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 <iostream>
using namespace std;
using ll = long long;

int main() {
    const int MN = 50, MX = MN;
    int N, A; cin >> N >> A;
    int x[MN];
    for (int i = 0; i < N; i++) cin >> x[i];

    ll dp[MN + 1][MN * MX + 1] = {};
    dp[0][0] = 1;
    for (int i = 0; i < N; i++) {
        for (int j = N; j >= 1; j--) {
            for (int k = x[i]; k <= MN * MX; k++) {
                dp[j][k] += dp[j - 1][k - x[i]];
            }
        }
    }

    ll ans = 0;
    for (int j = 1; j <= N; j++) {
        ans += dp[j][j * A];
    }
    cout << ans << endl;
    return 0;
}