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: Wrong Answer)

#include <bits/stdc++.h>
#define all(x) begin(x), end(x)
#define dbg(x) cerr << #x << " = " << x << endl
#define _ << ' ' <<
using namespace std;
using ll = long long;
using vi = vector<int>;

int n, a, x[50];
int dp[51][51][51 * 51];

int f(int k, int m, int s)
{
    if (k == n) return (m > 0 && s / m == a && s % m == 0);
    if (dp[k][m][s] != -1) return dp[k][m][s];
    return dp[k][m][s] = f(k + 1, m, s) + f(k + 1, m + 1, s + x[k]);
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> n >> a;
    for (int i = 0; i < n; ++i)
        cin >> x[i];

    memset(dp, -1, sizeof dp);
    cout << f(0, 0, 0);
}