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 AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var hw = Console.ReadLine().Split().Select(int.Parse).ToArray();
			int h = hw[0];
			int w = hw[1];
			if (h % 3 == 0 || w % 3 == 0) {
				Console.WriteLine(0);
				return;
			}

			long l = w > h ? w : h;
			long s = w > h ? h : w;
			long delta1;
			long delta2;
			{
				long ll = (l / 3);
				long r1 = s * ll;
				long r2 = (l - ll) * (s / 2);
				long r3 = (l - ll) * (s - (s / 2));
				long max = Math.Max(r1, Math.Max(r2, r3));
				long min = Math.Min(r1, Math.Min(r2, r3));
				delta1 = max - min;
			}

			{
				long ll = (l / 3) + 1;
				long r1 = s * ll;
				long r2 = (l - ll) * (s / 2);
				long r3 = (l - ll) * (s - (s / 2));
				long max = Math.Max(r1, Math.Max(r2, r3));
				long min = Math.Min(r1, Math.Min(r2, r3));
				delta2 = max - min;

			}

			Console.WriteLine(Math.Min(Math.Min(delta1, delta2), s));
		}
	}
}