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

namespace ABC_C
{
    class C062
    {        

        static long CalcMin(int h, int w)
        {
            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;
                }
            }
            return min;
        }

        static void Main(string[] args)
        {
            string[] s1 = Console.ReadLine().Split(' ');
            int h = int.Parse(s1[0]);
            int w = int.Parse(s1[1]);

            if (h % 3 == 0 || w % 3 == 0)
            {
                Console.WriteLine(0);
            }
            else
            {
                long m1 = CalcMin(w, h);
                long m2 = CalcMin(h, w);

                long m3 = Math.Min(h, w); //平行切り


                long min =Math.Min( Math.Min(m1, m2),m3);

                Console.WriteLine(min);
            }
        }
    }
}