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 static System.Math;
using static System.Console;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace AtCoder
{
	class Program
	{
		private static long max = long.MaxValue - (long)1e12 * (16 + 1);

		static void Main(string[] args)
		{
			var firstLine = ReadLine().Split(' ').Select(value => long.Parse(value)).ToArray();
			var h = firstLine[0];
			var w = firstLine[1];

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

			var blocks = h * w;
			var oneThirdBlocks = blocks / 3;
			var min = long.MaxValue;

			for(var i = 0; i < 2; i++)
			{
				var firstBlockH = oneThirdBlocks / w != 0 ? oneThirdBlocks / w : 1;
				firstBlockH += i;
				if(firstBlockH > h)
				{
					break;
				}
				var remainBlockH = h - firstBlockH;
				var firstBlocks = firstBlockH * w;
				var remainBlocks = blocks - firstBlocks;

				if(remainBlockH != 1)
				{
					var secondBlockH = remainBlockH / 2;
					var secondBlocks = secondBlockH * w;
					var thirdBlocks = (remainBlockH - secondBlockH) * w;

					min = Min(min, Max(firstBlocks, Max(secondBlocks, thirdBlocks)) - Min(firstBlocks, Min(secondBlocks, thirdBlocks)));
				}
				if(w != 1)
				{
					var secondBlockW = w / 2;
					var secondBlocks = remainBlockH * secondBlockW;
					var thirdBlocks = remainBlockH * (w - secondBlockW);

					min = Min(min, Max(firstBlocks, Max(secondBlocks, thirdBlocks)) - Min(firstBlocks, Min(secondBlocks, thirdBlocks)));
				}
			}

			for(var i = 0; i < 2; i++)
			{
				var firstBlockW = oneThirdBlocks / h != 0 ? oneThirdBlocks / h : 1;
				firstBlockW += i;
				if (firstBlockW > w)
				{
					break;
				}
				var remainBlockW = w - firstBlockW;
				var firstBlocks = firstBlockW * h;
				var remainBlocks = blocks - firstBlocks;

				if (remainBlockW != 1)
				{
					var secondBlockW = remainBlockW / 2;
					var secondBlocks = secondBlockW * h;
					var thirdBlocks = (remainBlockW - secondBlockW) * h;

					min = Min(min, Max(firstBlocks, Max(secondBlocks, thirdBlocks)) - Min(firstBlocks, Min(secondBlocks, thirdBlocks)));
				}
				if (h != 1)
				{
					var secondBlockH = h / 2;
					var secondBlocks = remainBlockW * secondBlockH;
					var thirdBlocks = remainBlockW * (h - secondBlockH);

					min = Min(min, Max(firstBlocks, Max(secondBlocks, thirdBlocks)) - Min(firstBlocks, Min(secondBlocks, thirdBlocks)));
				}
			}

			WriteLine(min);
		}
	}
}