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)

//#pragma warning disable

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

public class Test
{
    public static void Main()
    {
        var line1 = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        var H = line1[0];
        var W = line1[1];

        var answer = Math.Min(
            SubTask(H, W),
            SubTask(W, H));

        Console.WriteLine(answer);
    }

    public static long SubTask(long H, long W)
    {
        long Diffmin = long.MaxValue;

        {
            // 縦3分割
            long max = ((H + 2) / 3) * W;
            long min = (H / 3) * W;

            Diffmin = Math.Min(Diffmin, max - min);
        }
        {
            // 縦に分割してから横(1)
            long[] area = new long[] {
                ((H + 1) / 3) * W,
                (H - (H + 1) / 3) * (W / 2),
                (H - (H + 1) / 3) * ((W + 1) / 2),
            };

            area = area.OrderBy(x => x).ToArray();
            Diffmin = Math.Min(Diffmin, area[2] - area[0]);
        }
        {
            // 縦に分割してから横(2)
            long[] area = new long[] {
                ((H + 2) / 3) * W,
                (H - (H + 2) / 3) * (W / 2),
                (H - (H + 2) / 3) * ((W + 1) / 2),
            };

            area = area.OrderBy(x => x).ToArray();
            Diffmin = Math.Min(Diffmin, area[2] - area[0]);
        }

        return Diffmin;
    }
}