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;

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = ReadArrayInt();
            var H = input[0];
            var W = input[1];
            var ans = long.MaxValue;            
            for (long i = 1; i < W; i++)
            {
                long tmpMax = Math.Max(i * H, Math.Max((W - i) * (H / 2), (W - i) * (H - H / 2)));
                long tmpMin = Math.Min(i * H, Math.Min((W - i) * (H / 2), (W - i) * (H - H / 2)));
                if (tmpMax - tmpMin < ans) ans = tmpMax - tmpMin;
            }
            for (long i = 1; i < H; i++)
            {
                long tmpMax = Math.Max(i * W, Math.Max((H - i) * (W / 2), (H - i) * (W - W / 2)));
                long tmpMin = Math.Min(i * W, Math.Min((H - i) * (W / 2), (H - i) * (W - W / 2)));
                if (tmpMax - tmpMin < ans) ans = tmpMax - tmpMin;
            }
            for (long i = 1; i < W - 1; i++)
            {
                long tmpMax = Math.Max(i * H, Math.Max((W - i) / 2 * H, ((W - i) - (W - i) / 2) * H));
                long tmpMin = Math.Min(i * H, Math.Min((W - i) / 2 * H, ((W - i) - (W - i) / 2) * H));
                if (tmpMax - tmpMin < ans) ans = tmpMax - tmpMin;
            }
            for (long i = 1; i < H - 1; i++)
            {
                long tmpMax = Math.Max(i * W, Math.Max((H - i) / 2 * W, ((H - i) - (H - i) / 2) * W));
                long tmpMin = Math.Min(i * W, Math.Min((H - i) / 2 * W, ((H - i) - (H - i) / 2) * W));
                if (tmpMax - tmpMin < ans) ans = tmpMax - tmpMin;
            }

            Console.WriteLine(ans);
            Console.ReadLine();
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}