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: Accepted)

#include<iostream>

using namespace std;

int main(){
    long long int h, w, mn=100000000;
    cin >>h >> w;
    if(h%3==0 || w%3==0){
        mn = 0;
    }
    else{
        mn = min(mn, h);
        mn = min(mn, w);
        for(int i=1;i<w;i++){
            mn = min(mn, max(abs(i*h - (w-i)*(h/2)), max((w-i)*(h-(h/2))-i*h, (w-i)*(h-(h/2)) - (w-i)*(h/2))));
        }
        for(int i=1;i<h;i++){
            mn = min(mn, max(abs(i*w - (h-i)*(w/2)), max((h-i)*(w-(w/2))-i*w, (h-i)*(w-(w/2)) - (h-i)*(w/2))));
        }
    }
    cout << mn << endl;
}