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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AIZU
{
    class Program
    {
        static int cin() { return int.Parse(Console.ReadLine()); }
        static int cin(int D)
        {
            string s = Console.ReadLine();
            if (string.IsNullOrEmpty(s)) return D;
            return int.Parse(s);
        }
        static int[] cins()
        {
            string s = Console.ReadLine();
            if (string.IsNullOrEmpty(s)) return new int[] { };
            string[] ss = s.Split(' ');
            int[] Res = new int[ss.Length];
            for (int i = 0; i < ss.Length; i++) Res[i] = int.Parse(ss[i]);
            return Res;
        }
        static void print(object j) { Console.WriteLine(j.ToString()); }
        static void print(string j) { Console.WriteLine(j); }
        static void Main(string[] args)
        {
            int[] K = cins();
            int H = K[0], W = K[1];
            print(Exp(H, W));
            Console.ReadLine();
        }

        static int Exp(int H, int W)
        {
            int Res = int.MaxValue;
            if (H % 3 == 0 || W % 3 == 0) Res = 0;
            if (Res > W) Res = W;
            if (Res > H) Res = H;
            Res = Math.Min(split(H, W),Res);
            Res = Math.Min(split(W, H), Res);
            return Res;
        }

        static int split(int H,int W) {
            ulong[] D;
            ulong rl;
            bool even;
            D = new ulong[H];
            D[0] = ulong.MaxValue;
            if (W % 2 == 0)
            {
                rl = (ulong)Math.Min(-W * (H / 3) + (H - H / 3) * (W / 2), W * (H / 3 + 1) - (H - H / 3 - 1) * (W / 2));
            }
            else
            {
                Func<long, long> A = i => Math.Abs(i);
                long S0, S1, S2;
                for (int H0 = 1; H0 < H; H0++)
                {
                    S0 = W * H0;
                    S1 = (W + 1) / 2 * (H - H0);
                    S2 = (W - 1) / 2 * (H - H0);
                    D[H0] = (ulong)Math.Max(Math.Max(A(S0 - S1), A(S2 - S0)), H - H0);
                }
                rl = D.Min();
            }
            return (int)rl;
        }
    }
}