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

class Solve
{
	const int mod = 1000000007;
	static void Main(string[] args)
	{
		var input = Console.ReadLine().Split().Select(long.Parse).ToArray();
		long H = input[0];
		long W = input[1];
		long ans = H * W;
		if ((H * W) % 3 == 0) { ans = 0; }
        else
		{
            for(var i = 1; i < H; i++)
			{
				long s1 = i * W;
				long s2 = Math.Min((H - i) * ((W + 1) / 2), W * (H - i + 1) / 2);
				long s3 = H * W - s1 - s2;
				long dif = Math.Max(s1, Math.Max(s2, s3)) - Math.Min(s1, Math.Min(s2, s3));
				if (dif < ans) { ans = dif; }
			}
			for (var i = 1; i < W; i++)
			{
				long s1 = i * H;
				long s2 = Math.Min((W - i) * ((H + 1) / 2), H * (W - i + 1) / 2);
				long s3 = H * W - s1 - s2;
				long dif = Math.Max(s1, Math.Max(s2, s3)) - Math.Min(s1, Math.Min(s2, s3));
				if (dif < ans) { ans = dif; }
			}
		}
		Console.WriteLine(ans);
	}
}