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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Test1
{
	class Program
	{
		static void Main(string[] args)
		{
			String[] temp = Console.ReadLine().Split(' ');
			int H = int.Parse(temp[0]);
			int G = int.Parse(temp[1]);

			int diffMin = H * G;

			for (int i = 1; i < H; i++)
			{
				int[] s1 = { i * G, ((H - i) / 2) * G, (H - i) * G - ((H - i) / 2) * G };
				int diff1 = s1.Max() - s1.Min();
					diffMin = diff1 < diffMin ? diff1 : diffMin;
				int[] s2 = { i * G, (H - i) * (G / 2), (H - i) * G - (H - i) * (G / 2) };
				int diff2 = s2.Max() - s2.Min();
				diffMin = diff2 < diffMin ? diff2 : diffMin;
			}
			for (int i = 1; i < G; i++)
			{
				int[] s1 = { H * i, H * ((G - i) / 2), H * (G - i) - H * ((G - i) / 2) };
				int diff1 = s1.Max() - s1.Min();
				diffMin = diff1 < diffMin ? diff1 : diffMin;
				int[] s2 = { H * i, (H / 2) * (G - i), H * (G - i) - (H / 2) * (G - i) };
				int diff2 = s2.Max() - s2.Min();
				diffMin = diff2 < diffMin ? diff2 : diffMin;
			}

			Console.WriteLine (diffMin);
		}
	}
}