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 <iostream>
#include <algorithm>
using namespace std;

int main() {

    long long h, w;
    cin >> h >> w;

    long long ans = 1000000000000;
    if(h < w) swap(h, w);
    for(int i = 1; i < h; i++) {
        long long A = i * w;
        long long B = (h - i) * (w / 2);
        long long C = (h - i) * (w - w / 2);
        ans = min(ans, max(max(A, B), C) - min(min(A, B), C));
    }

    if(h > w) swap(h, w);
    for(int i = 1; i < h; i++) {
        long long A = i * w;
        long long B = (h - i) / 2 * w;
        long long C = ((h - i) - ((h - i) / 2)) * w;
        //cout << A << " " << B << " " << C << endl;
        ans = min(ans, max(max(A, B), C) - min(min(A, B), C));
    }
    cout << ans << endl;
}