Problem:
Score : 400 points

Problem Statement

There is a bar of chocolate with a height of H blocks and a width of W blocks.
Snuke is dividing this bar into exactly three pieces.
He can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.

Snuke is trying to divide the bar as evenly as possible.
More specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.
Find the minimum possible value of S_{max} - S_{min}.

Constraints

2 ≤ H, W ≤ 10^5

Input

Input is given from Standard Input in the following format:

H W

Output

Print the minimum possible value of S_{max} - S_{min}.

Sample Input 1

3 5

Sample Output 1

0

In the division below, S_{max} - S_{min} = 5 - 5 = 0.

Sample Input 2

4 5

Sample Output 2

2

In the division below, S_{max} - S_{min} = 8 - 6 = 2.

Sample Input 3

5 5

Sample Output 3

4

In the division below, S_{max} - S_{min} = 10 - 6 = 4.

Sample Input 4

100000 2

Sample Output 4

1

Sample Input 5

100000 100000

Sample Output 5

50000

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

using ll = long long;
#define ALL(c) (c).begin(), (c).end()
const int MOD = 1000000007;

int calc(int a, int b) {
    int mn = a * b;
    int t = a / 3;

    if (b % 2 == 0) {
        mn = min(mn, abs(t * b - ((a - t) * (b / 2))));
        mn = min(mn, abs((t + 1) * b - ((a - (t + 1)) * (b / 2))));
    } else {
        int x = t * b;
        int y = (a - t) * (b / 2);
        int z = (a - t) * (b / 2 + 1);
        mn = min({mn, max({abs(x - y), abs(x - z), abs(y - z)})});
        x = (t + 1) * b;
        y = (a - (t + 1)) * (b / 2);
        z = (a - (t + 1)) * (b / 2 + 1);
        mn = min({mn, max({abs(x - y), abs(x - z), abs(y - z)})});
    }

    return mn;
}

int main() {
    int h, w;
    cin >> h >> w; 

    if (h % 3 == 0 || w % 3 == 0) {
        cout << 0 << endl;
        return 0;
    }

    cout << min({h, w, calc(h, w), calc(w, h)}) << endl;

}