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.*;
import static java.lang.Integer.*;
import static java.lang.System.*;
import static java.lang.Math.*;

public class Main {
	public static void main(String[] args) {
		int i,j;
		Scanner sc = new Scanner(in);
		int h = parseInt(sc.next());
		int w = parseInt(sc.next());
		sc.close();
		int ans = 100000;
		if(h>=3) {
			int hmod = h % 3;
			switch(hmod) {
			case 0:
				ans = 0;
				break;
			case 1:
				if(w % 2 == 0) {
					ans = w/2;
				} else {
					ans = (w + (h - h/3 - 1))/2;
				}
				break;
			default:
				if(w % 2 == 0) {
					ans = w/2;
				} else {
					ans = (w + (h - h/3 - 1))/2;
				}
				break;
			}
		}
		int ans1 = 100000;
		if(w>=3) {
			int wmod = w % 3;
			switch(wmod) {
			case 0:
				ans1 = 0;
				break;
			case 1:
				if(h % 2 == 0) {
					ans1 = h/2;
				} else {
					ans1 = (h + (w - w/3 - 1))/2;
				}
				break;
			default:
				if(h % 2 == 0) {
					ans1 = h/2;
				} else {
					ans1 = (h + (w - w/3 - 1))/2;
				}
				break;
			}
		}
		ans = Math.min(ans, ans1);
		out.println(ans);
	}
}