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);
		int h = sc.nextInt();
		int w = sc.nextInt();
		System.out.println(Long.min(calc(h, w), calc(w, h)));
	}
	static long calc(long a, long b){
		long x = (a/3)*b;
		long y = ((a - a/3)/2)*b;
		long z = (a - (a/3) - (a - a/3)/2)*b;
		ArrayList<Long> vals = new ArrayList<>();
		vals.add(x); vals.add(y); vals.add(z);
		Collections.sort(vals);
		long min = vals.get(2) - vals.get(0);
		for(long i = 1; i < a-1; i++){
			x = i*b;
			y = (a-i)*(b/2);
			z = (a-i)*(b-b/2);
			vals = new ArrayList<>();
			vals.add(x); vals.add(y); vals.add(z);
			Collections.sort(vals);
			min = Long.min(min, vals.get(2) - vals.get(0));
		}
		return min;
	}
}