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;

public class Main {
	public static void main(String[] args){
		Scanner io = new Scanner(System.in);
		long H = io.nextLong();
		long W = io.nextLong();
		long sum = H*W;
		
		if(sum%3==0){
			System.out.println(0);
			return;
		}
		long ans = Long.MAX_VALUE;
		long x,y,z,max,min;
		for(int i=1;i<H;i++){
			x = W*i;
			y = (H-i)*(W/2);
			z = sum - x -y;
			max = Math.max(x,Math.max(y, z));
			min = Math.min(x,Math.min(y, z));
			ans = Math.min(ans,max-min);
			y = (H-i)/2*W;
			z = sum - x -y;
			max = Math.max(x,Math.max(y, z));
			min = Math.min(x,Math.min(y, z));
			ans = Math.min(ans,max-min);
		}
		for(int i=1;i<W;i++){
			x = H*i;
			y = (W-i)*(H/2);
			z = sum - x -y;
			max = Math.max(x,Math.max(y, z));
			min = Math.min(x,Math.min(y, z));
			ans = Math.min(ans,max-min);
			y = (W-1)/2*H;
			z = sum - x -y;
			max = Math.max(x,Math.max(y, z));
			min = Math.min(x,Math.min(y, z));
			ans = Math.min(ans,max-min);
		}
		System.out.println(ans);
	}
}