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;

class P
{
    static void Main()
    {
        long[] hw = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long res;
        if ((hw[1] % 3) * (hw[0] % 3) == 0)
        {
            res = 0;
        }
        else
        {
            long[] a = { hw[0] / 3 * hw[1], (hw[0] - hw[0] / 3) * (hw[1] / 2), (hw[0] - hw[0] / 3) * (hw[1] - hw[1] / 2) };
            long[] b = { (hw[0] / 3 + 1) * hw[1], (hw[0] - (hw[0] / 3 + 1)) * (hw[1] / 2), (hw[0] - (hw[0] / 3 + 1)) * (hw[1] - hw[1] / 2) };
            long[] c = { hw[1] / 3 * hw[0], (hw[1] - hw[1] / 3) * (hw[0] / 2), (hw[1] - hw[1] / 3) * (hw[0] - hw[0] / 2) };
            long[] d = { (hw[1] / 3 + 1) * hw[0], (hw[1] - (hw[1] / 3 + 1)) * (hw[0] / 2), (hw[1] - (hw[0] / 3 + 1)) * (hw[0] - hw[0] / 2) };
            res = Math.Min(Math.Min(a.Max() - a.Min(), b.Max() - b.Min()), Math.Min(c.Max() - c.Min(), d.Max() - d.Min()));
        }
        Console.WriteLine(res);
    }
}