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: Accepted)

using System;
using System.Linq;

namespace C
{
	internal class Program
	{
		private static int h;
		private static int w;

		public static void Main(string[] args)
		{
			var inputs = Console.ReadLine().Split().Select(int.Parse).ToArray();
			var saveH = h = inputs[0];
			var saveW = w = inputs[1];

			if (h % 3 == 0 || w % 3 == 0)
			{
				Console.WriteLine(0);
				return;
			}

			h -= h / 3;
			var result = solve(saveH / 3 * w);
			h--;
			result = Math.Min(result, solve((saveH / 3 + 1) * w));
			h = saveH;
			w -= w / 3;
			result = Math.Min(result, solve(saveW / 3 * h));
			w--;
			result = Math.Min(result, solve((saveW / 3 + 1) * h));

			Console.WriteLine(result);
		}

		public static long solve(long firstSquare)
		{
			if (h % 2 == 0) { return Math.Abs(firstSquare - h / 2 * w); }

			if (w % 2 == 0) { return Math.Abs(firstSquare - w / 2 * h); }

			if (h > w)
			{
				var tmp1 = Math.Abs(firstSquare - h / 2 * w);
				var tmp2 = Math.Abs(firstSquare - (h / 2 + 1) * w);

				return Math.Max(tmp1, tmp2);
			}
			else
			{
				var tmp1 = Math.Abs(firstSquare - w / 2 * h);
				var tmp2 = Math.Abs(firstSquare - (w / 2 + 1) * h);

				return Math.Max(tmp1, tmp2);
			}
		}
	}
}