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

namespace NotFounds
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            new Program().Solve(new ConsoleInput(Console.In, ' '));
            Console.Out.Flush();
        }

        public void Solve(ConsoleInput cin)
        {
            var H = cin.ReadLong;
            var W = cin.ReadLong;

            var diff = long.MaxValue;
            for (int i = 1; i < H; ++i)
            {
                var t1 = i * W;
                var x = (H - i) / 2;
                var t2 = x * W;
                var t3 = (H - i - x) * W;
                diff = Min(Max(Max(t1, t2), t3) - Min(Min(t1, t2), t3), diff);

                x = W / 2;
                t2 = (H - i) * x;
                t3 = (H - i) * (W - x);
                diff = Min(Max(Max(t1, t2), t3) - Min(Min(t1, t2), t3), diff);
            }
            for (int i = 1; i < W; ++i)
            {
                var t1 = i * H;
                var x = (W - i) / 2;
                var t2 = x * H;
                var t3 = (W - i - x) * H;
                diff = Min(Max(Max(t1, t2), t3) - Min(Min(t1, t2), t3), diff);

                x = H / 2;
                t2 = (W - i) * x;
                t3 = (W - i) * (H - x);
                diff = Min(Max(Max(t1, t2), t3) - Min(Min(t1, t2), t3), diff);
            }
            WriteLine(diff);
        }
    }

    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;}
        public void ReadIntArrays(long N, out int[] A, out int[] B) { A = new int[N]; B = new int[N]; for (long i = 0; i < N; ++i) { A[i] = ReadInt; B[i] = ReadInt; }}
        public void ReadLongArrays(long N, out long[] A, out long[] B) { A = new long[N]; B = new long[N]; for (long i = 0; i < N; ++i) { A[i] = ReadLong; B[i] = ReadLong; }}
    }
}