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;

long long int my_abs(long long int x){
    if(x < 0){
        return -x;
    }
    return x;
}

int main() {

    int h,w;

    cin >> h >> w;

    long long int ans = 1e12;

    if(h%3 == 0 || w%3 == 0){
        ans = 0;
    }
    else{


        for(int i=1; i<w-1; i++){
            long long int area1 = i*h;
            long long int area2 = (w-i)/2*h;
            long long int area3 = w*h - area1 - area2;
            long long int max_area = max(area1,max(area2,area3));
            long long int min_area = min(area1,min(area2,area3));
            ans = min(ans,max_area - min_area);
            
            area2 = h/2*(w-i);
            area3 = w*h - area1 - area2;
            max_area = max(area1,max(area2,area3));
            min_area = min(area1,min(area2,area3));
            ans = min(ans,max_area - min_area);

        }

        for(int i=1; i<h-1; i++){
            long long int area1 = i*w;
            long long int area2 = (h-i)/2*w;
            long long int area3 = w*h - area1 - area2;
            long long int max_area = max(area1,max(area2,area3));
            long long int min_area = min(area1,min(area2,area3));
            ans = min(ans,max_area - min_area);

            area2 = w/2*(h-i);
            area3 = w*h - area1 - area2;
            max_area = max(area1,max(area2,area3));
            min_area = min(area1,min(area2,area3));
            ans = min(ans,max_area - min_area);
        }
        
    }

    cout << ans << endl;

    return 0;
}