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 ABC_C
{
    class C062
    {
        static void Main(string[] args)
        {
            string[] s1 = Console.ReadLine().Split(' ');
            int H = int.Parse(s1[0]);
            int W = int.Parse(s1[1]);

            int h = Math.Min(H, W);
            int w = Math.Max(H, W);

            if (h % 3 == 0 || w % 3 == 0)
            {
                Console.WriteLine(0);
            }
            else
            {
                long min = long.MaxValue;

                for (int i = 1; i < w; i++)
                {
                    long S1 = (long)i * h;
                    int cut = h / 2;
                    long S2 = (long)(w - i) * cut;
                    long S3 = (long)(w - i) * (h - cut);
                    long Smax = Math.Max(S1, S3);
                    long Smin = Math.Min(S1, S2);
                    if (min > Smax - Smin)
                    {
                        min = Smax - Smin;
                    }
                }

                Console.WriteLine(min);
            }
        }
    }
}