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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

    private static long max(long a, long b, long c) {
        return Math.max(a, Math.max(b, c));
    }

    private static long min(long a, long b, long c) {
        return Math.min(a, Math.min(b, c));
    }

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        long h = s.nextLong();
        long w = s.nextLong();
        long min = Long.MAX_VALUE;
        for (int i = 1; i < h; i++) {
            long sa = i * w;
            long sbv = ((h - i) / 2) * w;
            long scv = (h - i - (h - i) / 2) * w;
            long sbh = (h - i) * (w / 2);
            long sch = (h - i) * (w - (w / 2));
            min = Math.min(max(sa, sbv, scv) - min(sa, sbv, scv), min);
            min = Math.min(max(sa, sbh, sch) - min(sa, sbh, sch), min);
        }
        for (int i = 1; i < w; i++) {
            long sa = h * i;
            long sbv = h * ((w - i) / 2);
            long scv = h * (w - i - (w - i) / 2);
            long sbh = (h / 2) * (w - i);
            long sch = (h - (h / 2)) * (w - i);
            min = Math.min(max(sa, sbv, scv) - min(sa, sbv, scv), min);
            min = Math.min(max(sa, sbh, sch) - min(sa, sbh, sch), min);
        }
        System.out.println(min);
    }

}