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.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long h = sc.nextLong(),w = sc.nextLong();
		long s1 = 0, s2 = 0, s3 = 0;
		long min = Long.MAX_VALUE;
		for (int i = 1; i < w; i++) {
			s1 = i*h;
			s2 = h/2*(w-i);
			s3 = (h+1)/2*(w-i);
			min = Math.min(min, Math.max(Math.max(s1,s2),s3)-Math.min(Math.min(s1,s2),s3));
			s2 = (w-i)/2*h;
			s3 = (w-i+1)/2*h;
			min = Math.min(min, Math.max(Math.max(s1,s2),s3)-Math.min(Math.min(s1,s2),s3));
		}
		for (int i = 1; i < h; i++) {
			s1 = i*w;
			s2 = w/2*(h-i);
			s3 = (w+1)/2*(h-i);
			min = Math.min(min, Math.max(Math.max(s1,s2),s3)-Math.min(Math.min(s1,s2),s3));
			s2 = (h-i)/2*w;
			s3 = (h-i+1)/2*w;
			min = Math.min(min, Math.max(Math.max(s1,s2),s3)-Math.min(Math.min(s1,s2),s3));
		}
		System.out.println(min);
		sc.close();
	}
}