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 Yorukatsu048.Questions;
using Yorukatsu048.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace Yorukatsu048.Questions
{
    /// <summary>
    /// ARC074 C
    /// </summary>
    public class QuestionE : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var hw = inputStream.ReadIntArray();
            long height = hw[0];
            long width = hw[1];

            long min = Math.Min(Math.Min(Math.Min(GetDiff3(height, width), GetDiff3(width, height)), GetDiff2And1(height, width)), GetDiff2And1(width, height));
            yield return min;
        }

        long GetDiff3(long height, long width)
        {
            long min = long.MaxValue;
            for (int i = 1; i * 2 < height; i++)
            {
                min = Math.Min(min, Math.Abs(i - (height - 2 * i)) * width);
            }
            return min;
        }

        long GetDiff2And1(long height, long width)
        {
            long overallMin = long.MaxValue;
            for (int i = 0; i < height; i++)
            {
                var s1 = i * width;
                var w2 = width / 2;
                var w3 = width - w2;
                var h = height - i;
                var s2 = w2 * h;
                var s3 = w3 * h;
                var max = Math.Max(s1, Math.Max(s2, s3));
                var min = Math.Min(s1, Math.Min(s2, s3));
                overallMin = Math.Min(overallMin, max - min);
            }
            return overallMin;
        }
    }
}


namespace Yorukatsu048
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionE();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace Yorukatsu048.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace Yorukatsu048.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion