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.Generic;
using System.IO;
using System.Linq;
using System.Runtime.Serialization.Formatters.Binary;
using System.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
using System.Numerics;
using System.Collections;

static class MainClass
{
    public static void Main(string[] args)
    {
        var HW = Console.ReadLine().SplittedStringToBigInteger();
        var H = HW[0];
        var W = HW[1];
        BigInteger minimumdiff = LONGINF;
        for (int i = 1; i <= H; i++)
        {
            var num1 = i * W;
            var num2 = (W / 2) * (H - i);
            var num3 = (W - (W / 2)) * (H - i);
            var max = BigInteger.Max(num1, BigInteger.Max(num2, num3));
            var min = BigInteger.Min(num1, BigInteger.Min(num2, num3));
            minimumdiff = BigInteger.Min(max - min, minimumdiff);
        }
        for (int i = 0; i <= W; i++)
        {
            var num1 = i * H;
            var num2 = (H / 2) * (W - i);
            var num3 = (H - (H / 2)) * (W - i);
            var max = BigInteger.Max(num1, BigInteger.Max(num2, num3));
            var min = BigInteger.Min(num1, BigInteger.Min(num2, num3));
            minimumdiff = BigInteger.Min(max - min, minimumdiff);
        }
        minimumdiff = BigInteger.Min(minimumdiff, H % 3 == 0 ? 0 : W);
        minimumdiff = BigInteger.Min(minimumdiff, W % 3 == 0 ? 0 : H);

        Console.WriteLine(minimumdiff);
        Console.ReadLine();
    }

    public static void PrintArray<T>(T[,] array)
    {
        for (int i = 0; i < array.GetLength(0); i++)
        {
            for (int j = 0; j < array.GetLength(1); j++)
            {
                Console.Write(array[i, j] + " ");
            }
            Console.WriteLine();
        }
    }

    #region ライブラリ
    public static long ToInt64(this string str) => long.Parse(str);
    public static int ToInt32(this string str) => int.Parse(str);
    public static BigInteger ToBigInteger(this string str) => BigInteger.Parse(str);
    public static List<string> SplittedStringToList(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).ToList();
    public static List<int> SplittedStringToInt32List(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => int.Parse(x)).ToList();
    public static List<BigInteger> SplittedStringToBigInteger(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => BigInteger.Parse(x)).ToList();
    public const int INF = int.MaxValue / 2;
    public const long LONGINF = long.MaxValue / 2;

    public static int Max(params int[] values)
    {
        var maxes = -1;
        for (int i = 0; i < values.Length; i++)
        {
            maxes = Math.Max(values[i], maxes);
        }
        return maxes;
    }

    #endregion
}