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.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;
using System.Text;
using System.Diagnostics;

class Program
{
    static void Main()
    {
        long[] hw = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long h = hw[0];
        long w = hw[1];
        long ans = 99999999999999;

        if (h % 3 == 0 || w % 3 == 0)
        {
            Console.WriteLine(0);
            return;
        }

        long starth = h / 3 == 0 ? 1 : h / 3;
        long startw = w / 2 == 0 ? 1 : w / 2;

        for (long i = starth; i < starth + 3 && i < h; i++)
        {
            for (long j = startw; j < startw + 2 && j < w; j++)
            {
                long s1 = 0;
                long s2 = 0;
                long s3 = 0;

                s1 = i * w;
                s2 = (h - i) * j;
                s3 = (h - i) * (w - j);

                long smax = Math.Max(s1, Math.Max(s2, s3));
                long smin = Math.Min(s1, Math.Min(s2, s3));

                ans = Math.Min(ans, (smax - smin));
            }
        }

        starth = h / 2 == 0 ? 1 : h / 2;
        startw = w / 3 == 0 ? 1 : w / 3;

        for (long i = starth; i < starth + 2 && i < h; i++)
        {
            for (long j = startw; j < startw + 3 && j < w; j++)
            {
                long s1 = 0;
                long s2 = 0;
                long s3 = 0;

                s1 = j * h;
                s2 = (w - j) * i;
                s3 = (w - j) * (h - i);

                long smax = Math.Max(s1, Math.Max(s2, s3));
                long smin = Math.Min(s1, Math.Min(s2, s3));

                ans = Math.Min(ans, (smax - smin));
            }
        }

        Console.WriteLine(ans);
    }
}