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 {
	static long ans = Integer.MAX_VALUE;
	static long s;
	public static void main(String[] args) {
		final Scanner sc = new Scanner(System.in);
		long h = sc.nextLong();
		long w = sc.nextLong();
		long s1, s2;
		s = h * w;
		for(int i = 0; i <= h; i++) {
			s1 = w * i;
			s2 = w * (h-i)/2;
			update(s1, s2);
			s2 = (h - i) * (w / 2);
			update(s1, s2);
		}
		for(int i = 0; i <= w; i++) {
			s1 = h * i;
			s2 = h * (w - i)/2;
			update(s1, s2);
			s2 = (h / 2) * (w - i);
			update(s1, s2);
		}
		System.out.println(ans);
	}
	static void update(long s1, long s2) {
		if(s1 == 0 || s2 == 0) {
			return;
		}
		long s3 = - s1 - s2 + s;
		long sa = Math.max(s1, Math.max(s2, s3)) - Math.min(s1, Math.min(s2, s3));
		if(ans > sa) {
			ans = sa;
		}
	}
}