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 static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;

class Program
{
    static void Main(string[] args)
    {
        var hw = Array.ConvertAll(ReadLine().Split(' '), long.Parse);
        var res = long.MaxValue;
        for (var j = 0; j < 2; j++)
            for (var i = 1; i < hw[j]; i++)
            {
                var ar = new[] { i * hw[(j + 1) % 2], (hw[j] - i) * (hw[(j + 1) % 2] / 2), (hw[j] - i) * ((hw[(j + 1) % 2] + 1) / 2) };
                var ar2 = new[] { i * hw[(j + 1) % 2], hw[(j + 1) % 2] * ((hw[j] - i + 1) / 2), hw[(j + 1) % 2] * ((hw[j] - i) / 2) };
                res = Min(res, ar.Max() - ar.Min());
                res = Min(res, ar2.Max() - ar2.Min());
            }
        WriteLine(res);
    }
    private const string ALFA = "abcdefghijklmnopqrstuvwxyz";
    private const int MOD = 1000000007;
}