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.Scanner;

/**
 * https://abc062.contest.atcoder.jp/tasks/arc074_a
 */
public class Main {

	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		int H = sc.nextInt();
		int W = sc.nextInt();
		sc.close();
		
		long ans = Math.min((H%3)*W,(W%3)*H);
		ans = Math.min(ans, getAreaDiff(W,H));
		ans = Math.min(ans, getAreaDiff(H,W));
		
		System.out.println(ans);
		
	}
	
	static long getAreaDiff(long w, long h){
		long diff = h*w;
		for(int i=1; i<h; i++){
			long h1 = i;
			long h2 = h-i;
			long w1 = w/2;
			long w2 = w-w1;
			long area = (long) Math.max(h1*w, h2*w2) - Math.min(h1*w, h2*w1);
			diff = Math.min(diff, area);
		}
		return diff;
	}

}