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-csc 3.5.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;
using static System.Console;
using static System.Math;

namespace Atcoder
{
    class Program
    {
        static StreamWriter sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
        static void Main(string[] args)
        {
            try
            {
                SetOut(sw);
                Solve.Answer();
                Out.Flush();
            }
            catch (Exception ex)
            {
                WriteLine(ex.ToString());
            }
        }
    }

    public class Solve
    {
        public static void Answer()
        {
            var HW = IO.RSLong;
            var H = HW[0];
            var W = HW[1];

            var ans = 100100100l;
            for (int i = 1; i < H; i++)
            {
                var now_H = H - i;
                var S1 = i * W;
                var S2 = 0l;
                var S3 = 0l;
                if (W % 2 == 0 || now_H % 2 == 0)
                {
                    S2 = W * now_H / 2;
                    S3 = W * now_H / 2;
                }
                else
                {

                    S2 = W / 2 * now_H;
                    S3 = (W / 2 + 1) * now_H;

                    var min1 = Min(S1, Min(S2, S3));
                    var max1 = Max(S1, Max(S2, S3));
                    ans = Min(ans, max1 - min1);


                    S2 = W * now_H / 2;
                    S3 = W * (now_H / 2 + 1);
                    var min2 = Min(S1, Min(S2, S3));
                    var max2 = Max(S1, Max(S2, S3));
                    ans = Min(ans, max2 - min2);

                }
                var min = Min(S1, Min(S2, S3));
                var max = Max(S1, Max(S2, S3));
                ans = Min(ans, max - min);
            }
            for (int i = 0; i < W; i++)
            {
                var now_W = W - i;
                var S1 = i * H;
                var S2 = 0l;
                var S3 = 0l;
                if (H % 2 == 0 || now_W % 2 == 0)
                {
                    S2 = H * now_W / 2;
                    S3 = H * now_W / 2;
                }
                else
                {
                    S2 = H / 2 * now_W;
                    S3 = (H / 2 + 1) * now_W;
                    var min1 = Min(S1, Min(S2, S3));
                    var max1 = Max(S1, Max(S2, S3));
                    ans = Min(ans, max1 - min1);

                    S2 = H * now_W / 2;
                    S3 = H * (now_W / 2 + 1);
                    var min2 = Min(S1, Min(S2, S3));
                    var max2 = Max(S1, Max(S2, S3));
                    ans = Min(ans, max2 - min2);

                }
                var min = Min(S1, Min(S2, S3));
                var max = Max(S1, Max(S2, S3));
                ans = Min(ans, max - min);
            }
            WriteLine(ans);
        }


    }

    public class IO
    {
        #region Input
        public static int RInt => int.Parse(ReadLine());
        public static long RLong => long.Parse(ReadLine());
        public static double RDouble => double.Parse(ReadLine());

        public static string[] RSString => ReadLine().Split();
        public static int[] RSInt => ReadLine().Split().Select(s => int.Parse(s)).ToArray();
        public static long[] RSLong => ReadLine().Split().Select(s => long.Parse(s)).ToArray();
        public static double[] RSDouble => ReadLine().Split().Select(s => double.Parse(s)).ToArray();
        #endregion

        #region Output
        public static void OutJoinSpace<T>(IEnumerable<T> list) => WriteLine(string.Join(" ", list));
        public static void WriteLineYes_or_No(bool flag) => WriteLine(flag ? "Yes" : "No");
        public static void WriteLineYES_or_NO(bool flag) => WriteLine(flag ? "YES" : "NO");
        #endregion
    }

    public class Mod
    {
        #region
        private readonly static long M = 1000000007;

        public static long Add(long a, long b) => (a * b) % M;
        public static long Sub(long a, long b) => (a - b) % M >= 0 ? (a - b) % M : (a - b) % M + M;
        public static long Multi(long a, long b) => (a * b) % M;
        #endregion
    }
}