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 {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		long w = sc.nextInt();
		long h = sc.nextInt();
		
		if(w%3==0 || h%3==0)
			System.out.println(0);
		else
			System.out.println(Math.min(solve(w, h), solve(h, w)));

	}
	static long solve(long w, long h){
		long min = Long.MAX_VALUE;
		for(int i=1;i<h;i++){
			long a = w*i;
			long b = w/2*(h-i);
			long c = 0;
			if(w%2==0)
				c = w/2*(h-i);
			else
				c = (w/2+1)*(h-i);
			
			long d = Math.max(a, Math.max(b, c))-Math.min(a, Math.min(b, c));
			if(d<min)
				min = d;
		}
		return min;
	}
}