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: Time Limit Exceeded)

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 = H / 3; i < H; i++)
			{
				for (int j = 1; j < (H - i); j++)
				{
					int[] s = { i * G, j * G, (H - i - j) * G };
					int dff = s.Max() - s.Min();
					diffMin = dff < diffMin ? dff : diffMin;
				}
				for (int j = 1; j < G; j++)
				{
					int[] s = { i * G, (H - i) * j, (H - i) * (G - j) };
					int dff = s.Max() - s.Min();
					diffMin = dff < diffMin ? dff : diffMin;
				}
			}
			for (int i = 1; i < G; i++)
			{
				for (int j = 1; j < (G - i); j++)
				{
					int[] s = { H * i, H * j, H  * (H - i - j) };
					int dff = s.Max() - s.Min();
					diffMin = dff < diffMin ? dff : diffMin;
				}
				for (int j = 1; j < H; j++)
				{
					int[] s = { H * i, j * (G - i), (H - j) * (G - i) };
					int dff = s.Max() - s.Min();
					diffMin = dff < diffMin ? dff : diffMin;
				}
			}

			Console.WriteLine (diffMin);
		}
	}
}