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 AtTest.C_Challenge
{
    class ABC_062
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            long h = long.Parse(input[0]);
            long w = long.Parse(input[1]);
            if (h % 3 == 0 || w % 3 == 0)
            {
                Console.WriteLine(0);
            }
            else
            {
                var margin = new long[4];
                //タテ3分割
                margin[0] = w;
                //ヨコ3分割
                margin[1] = h;

                //タテ1ヨコ2
                long h1 = h / 2;
                long h2 = (h + 1) / 2;
                for (int i = 1; i < w; i++)
                {
                    var tempArea = new long[3];
                    tempArea[0] = h * i;
                    tempArea[1] = h1 * (w - i);
                    tempArea[2] = h2 * (w - i);
                    long newMargin = tempArea.Max() - tempArea.Min();
                    if (margin[2] == 0 || newMargin < margin[2])
                    {
                        margin[2] = newMargin;
                    }
                }

                //タテ2ヨコ1
                long w1 = w / 2;
                long w2 = (w + 1) / 2;
                for (int i = 1; i < h; i++)
                {
                    var tempArea = new long[3];
                    tempArea[0] = w * i;
                    tempArea[1] = w1 * (h - i);
                    tempArea[2] = w2 * (h - i);
                    long newMargin = tempArea.Max() - tempArea.Min();
                    if (margin[3] == 0 || newMargin < margin[3])
                    {
                        margin[3] = newMargin;
                    }
                }
                Console.WriteLine(margin.Min());
            }
        }
    }
}