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;
public class MainApp
{
    static public void Main(string[] args)
    {
        var read = Console.ReadLine();
        var split = read.Split(' ');
        int H = int.Parse(split[0]);
        int W = int.Parse(split[1]);
        long output_min = H/2;
        output_min *= W;
        for (int c = 1; c < H / 2 +3; c++)
        {
            long area1 = W;
            area1 *= c;
            long area2 = H - c;
            long area3 = H - c;
            int Hl = W / 2;
            area2 *= W - Hl;
            area3 *= Hl;
            long max = Math.Max(Math.Max(area1, area2), area3);
            long min = Math.Min(Math.Min(area1, area2), area3);
            if (max - min < output_min)
            {
                output_min = max - min;
            }

        }
        for (int c = 1; c < W / 2 +3; c++)
        {
            long area1 = H;
            area1 *= c;
            long area2 = W - c;
            long area3 = W - c;
            int Wl = H / 2;
            area2 *= H - Wl;
            area3 *= Wl;
            long max = Math.Max(Math.Max(area1, area2), area3);
            long min = Math.Min(Math.Min(area1, area2), area3);
            if (max - min < output_min)
            {
                output_min = max - min;
            }

        }
        if (H % 3 == 0)
            output_min = 0;
        if (W % 3 == 0)
            output_min = 0;
        Console.WriteLine(output_min);
    }

}