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.Linq;
using System.IO;
using System.Text;
using System.Collections;
using System.Collections.Generic;
using System.Text.RegularExpressions;
 
class Program
{
    static void Main()
    {
        string[] inputs = Console.ReadLine().Split(' ');
        int H = int.Parse(inputs[0]);
        int W = int.Parse(inputs[1]);
        long result = 0;
        if (!(H % 3 == 0 || W % 3 == 0))
        {
            result = Math.Min(SearchMinimumDifference(H, W), SearchMinimumDifference(W, H));
            result = Math.Min(result, Math.Min(H, W));
        }
        Console.WriteLine(result);
    }

    static long SearchMinimumDifference(int H, int W)
    {
        long separatePoint = W / 3;
        long difference = long.MaxValue;
        bool isIncrease = true;
        do
        {
            long newDifference = CalculateDifference(H, W, separatePoint);
            Console.Error.WriteLine(": {0}", newDifference);
            if (difference > newDifference)
            {
                difference = newDifference;
                if (isIncrease) separatePoint++;
                else separatePoint--;
            }
            else if (isIncrease) isIncrease = false;
            else break;
        } while (separatePoint > 0 && separatePoint <= W / 2);
        return difference;
    }

    static long CalculateDifference(int H, int W, long separatePoint)
    {
        long[] areas = new long[3];
        areas[0] = H * separatePoint;
        long H2 = H / 2, W2 = W - separatePoint;
        areas[1] = H2 * W2;
        areas[2] = (H - H2) * W2;
        Console.Error.WriteLine(string.Join(" ", areas));
        return areas.Max() - areas.Min();
    }
}