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;
using System.Collections.Generic;
using System.Text;


class Program
{
    static void Main(string[] args)
    {
        // 入力
        //var s = Console.ReadLine();
        //var n = int.Parse(Console.ReadLine());
        int[] hw = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var h = hw[0];
        var w = hw[1];

        //分割方法は4パターン
        //初めに2パターン
        var s1 = 0;
        var s2 = 0;
        var s3 = 0;
        var h1 = 1;
        var max = 0;
        var min = 0;
        var ans = int.MaxValue;
        for (h1 = 1; h1 < h; h1++)
        {
            //残りの二つを横に分割するパターン
            s1 = h1 * w;
            s2 = (h - h1) / 2 * w;
            s3 = h * w - s1 - s2;
            max = Math.Max(Math.Max(s1, s2), s3);
            min = Math.Min(Math.Min(s1, s2), s3);
            ans = Math.Min(ans, max - min);

            //残りの二つを縦に分割するパターン
            s1 = h1 * w;
            s2 = (h - h1) * (int)Math.Floor((double)w / (double)2);
            s3 = h * w - s1 - s2;
            max = Math.Max(Math.Max(s1, s2), s3);
            min = Math.Min(Math.Min(s1, s2), s3);
            ans = Math.Min(ans, max - min);
        }

        var w1 = 1;
        for (w1 = 1; w1 < w; w1++)
        {
            //残りの二つを横に分割するパターン
            s1 = w1 * h;
            s2 = (w - w1) / 2 * h;
            s3 = h * w - s1 - s2;
            max = Math.Max(Math.Max(s1, s2), s3);
            min = Math.Min(Math.Min(s1, s2), s3);
            ans = Math.Min(ans, max - min);

            //残りの二つを縦に分割するパターン
            s1 = w1 * h;
            s2 = (w - w1) * (int)Math.Floor((double)h / (double)2);
            s3 = h * w - s1 - s2;
            max = Math.Max(Math.Max(s1, s2), s3);
            min = Math.Min(Math.Min(s1, s2), s3);
            ans = Math.Min(ans, max - min);
        }

        // 出力
        Console.WriteLine(ans);
    }
}