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.Linq;
using System.Collections.Generic;

public class Program
{
    public static void Main()
    {
        var hw = Console.ReadLine().Split()
            .Select(x => int.Parse(x))
            .OrderBy(x => x)
            .ToArray();

        if (hw.Any(x => x % 3 == 0))
        {
            Console.WriteLine(0);
            return;
        }

        var d = int.MaxValue;
        var s = hw[0] * hw[1];

        for (int i = 1; i < hw[1]; ++i)
        {
            var ss = new int[3];
            ss[0] = hw[0] * i;
            var h = hw[1] - i;
            ss[1] = hw[0] % 2 == 0
                ? hw[0] / 2 * h
                : h % 2 == 0
                ? h / 2 * hw[0]
                : Math.Max(hw[0], h) / 2 * Math.Min(hw[0], h);
            ss[2] = s - ss[0] - ss[1];

            d = Math.Min(d, ss.Max() - ss.Min());
        }
        Console.WriteLine(d);
    }
}