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.*;

public class Main {
	private static Scanner sc = new Scanner(System.in);
	public static void main(String[] args) {
		long h = sc.nextLong();
		long w = sc.nextLong();
		if (h%3==0||w%3==0) {
			System.out.println(0);
			return;
		}
		long ret = Integer.MAX_VALUE;
		ret = Math.min(ret, c1(h,w));
		ret = Math.min(ret, c1(w,h));
		System.out.println(ret);
	}

	private static long c1(long h, long w) {
		long tw = w/2;
		long a = 0;
		long b = 0;
		long c = 0;
		boolean bl = false;
		long ret = Integer.MAX_VALUE;
		for (int i = 1;i < h;i++) {
			a = i*w;
			b = (h-i)*tw;
			c = h*w-(a+b);
			ret = Math.min(ret, Math.max(a,Math.max(b,c))-Math.min(a,Math.min(b,c)));
		}
		return ret;
	}
}