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: Runtime Error)

#include <bits/stdc++.h>

using namespace std;

int l, n, q;
int x[100005];
int par[100005];
int pare[21][100005];

void initt()
{
    memset(pare, -1, sizeof(pare));
    for (int i = 1; i <= n; i++){
        pare[i][0] = par[i];
    }
    for (int j = 1; 1 << j < n; j++){
        for (int i = 1; i <= n; i++){
            if (pare[i][j-1] != -1)
                pare[i][j] = pare[pare[i][j-1]][j-1];
        }
    }
}

signed main() {
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
        scanf("%d", &x[i]);
    }
    x[n+1] = INT_MAX;
    scanf("%d%d", &l, &q);
    int ri = 1;
    for (int i = 1; i <= n; i++) {
        while (x[ri] - x[i] <= l) ri++; ri--;
        par[i] = ri;
    }
    initt();
    int a, b;
    for (int i = 1; i <= q; i++) {
        scanf("%d%d", &a, &b);
        if (a == b) {
            cout << 0 << "\n";
            continue;
        }
        if (a > b) swap(a, b);
        int res = 0;
        for (int j = 20; j >= 0; j--) {
            if (pare[a][j] < b && pare[a][j] != -1)
            {
                a = pare[a][j];
                res += 1 << j;
            }
        }
        res += 1;
        printf("%d\n", res);
    }
}