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: Accepted)

import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long H = sc.nextInt();
        long W = sc.nextInt();

        long ans = Math.min(H, W);
        if (H%3==0 || W%3==0) ans = 0;

        long w = W/2;
        long h = H*W/3/w;
        for (int i=(int)w-10;i<(int)w+10;i++) {
            for (int j=(int)h-10;j<(int)h+10;j++) {
                if (i<=0 || i>=W) continue;
                if (j<=0 || j>=H) continue;
                long[] area = new long[3];
                area[0] = (long)i*j;
                area[1] = (W-i)*j;
                area[2] = W*(H-j);
                Arrays.sort(area);
                ans = Math.min(ans, area[2]-area[0]);
            }
        }

        long y = H/2;
        long x = H*W/3/y;
        for (int i=(int)x-10;i<(int)x+10;i++) {
            for (int j=(int)y-10;j<(int)y+10;j++) {
                if (i<=0 || i>=W) continue;
                if (j<=0 || j>=H) continue;
                long[] area = new long[3];
                area[0] = i*j;
                area[1] = i*(H-j);
                area[2] = (W-i)*H;
                Arrays.sort(area);
                ans = Math.min(ans, area[2]-area[0]);
            }
        }
        System.out.println(ans);
    }
}