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.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCorder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
        }

        public void Solve(ConsoleInput cin)
        {
            var H = cin.ReadInt;
            var W = cin.ReadInt;
            var p = new long[3];
            var ans = long.MaxValue;

            if(H % 3 == 0 || W % 3 == 0)
            {
                WriteLine(0);
                return;
            }

            for(int i = 1; i <= W - 1; i++)
            {
                p[0] = i * H;
                var w = (W - i) / 2;
                p[1] = w * H;
                p[2] = H * (W - i - w);
                if (ans > p.Max() - p.Min()) ans = p.Max() - p.Min();
            }
            for(int i = 1; i <= W - 1; i++)
            {
                p[0] = H * i;
                var h = H / 2;
                p[1] = (W - i) * h;
                p[2] = (W - i) * (H - h);
                if (ans > p.Max() - p.Min()) ans = p.Max() - p.Min();
            }
            for(int i = 0; i <= H - 1; i++)
            {
                p[0] = W * i;
                var h = (H - i) / 2;
                p[1] = W * h;
                p[2] = W * (H - i - h);
                if (ans > p.Max() - p.Min()) ans = p.Max() - p.Min();
            }
            for(int i = 0; i <= H - 1; i++)
            {
                p[0] = W * i;
                var w = W / 2;
                p[1] = (H - i) * w;
                p[2] = (H - i) * (W - w);
                if (ans > p.Max() - p.Min()) ans = p.Max() - p.Min();
            }

            WriteLine(ans);
        }



        public long C(int X, int Y)
        {

            if (Y == 0 || Y == X)
            {
                return 1;
            }
            if (X < Y)
            {
                return 0;
            }
            var Pascal = new long[X + 1, X + 1];
            for (int i = 0; i <= X; i++)
            {
                Pascal[i, 0] = 1L;
                Pascal[i, i] = 1L;
            }
            for (int i = 2; i <= X; i++)
            {
                for (int j = 1; j < i; j++)
                {
                    Pascal[i, j] = Pascal[i - 1, j] + Pascal[i - 1, j - 1];
                }
            }
            return Pascal[X, Y];
        }

        public class ConsoleInput
        {
            private readonly System.IO.TextReader _stream;
            private char _separator = ' ';
            private Queue<string> inputStream;
            public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
            {
                this._separator = separator;
                this._stream = stream;
                inputStream = new Queue<string>();
            }
            public string Read
            {
                get
                {
                    if (inputStream.Count != 0) return inputStream.Dequeue();
                    string[] tmp = _stream.ReadLine().Split(_separator);
                    for (int i = 0; i < tmp.Length; ++i)
                        inputStream.Enqueue(tmp[i]);
                    return inputStream.Dequeue();
                }
            }
            public string ReadLine { get { return _stream.ReadLine(); } }
            public int ReadInt { get { return int.Parse(Read); } }
            public long ReadLong { get { return long.Parse(Read); } }
            public double ReadDouble { get { return double.Parse(Read); } }
            public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
            public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
            public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
        }
    }
}