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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int H = sc.nextInt();
        int W = sc.nextInt();
        if(H%3 == 0 || W%3 == 0){
            System.out.println(0);
            return;
        }
        int ans = Math.min(H, W);
        // for(int h = 1;h < H;h++){
        //     int l = 1;
        //     int h1 = Math.max(h, H-h);
        //     int h2 = Math.min(h, H-h);
        //     int d = h1*(W-2);
        //     l += d/(W+h1);
        //     ans = Math.min(ans, H*(W-l)-h2*l);
        //     l++;
        //     ans = Math.min(ans, h1*l-H*(W-l));
        //     ans = Math.min(ans, l*(h1-h2));
        //     ans = Math.min(ans, Math.abs((H-h)*W-h*(W/2)));
        //     ans = Math.min(ans, Math.abs((H-h)*W-h*((W+1)/2)));
        // }
        System.out.println(ans);
    }
}