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.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;
            var sum = W * H;
            //Ver and Ver
            if (Res > W) Res = W;
            //Hor and Hor
            if (Res > H) Res = H;
            //Ver and Hor
            long[] D;
            long rl;
            bool even;
            D = new long[H];
            D[0] = long.MaxValue;
            even = W % 2 == 0;
            if (even)
            {
                rl = Math.Min(-W*(H/3)+(H-H/3)*(W/2), W * (H / 3+1) - (H - H / 3-1) * (W / 2));
                goto HKJ;
            }
            else
            {
                bool b01, b02;
                for (int H0 = 1; H0 < H; H0++)
                {
                    b01 = (W + 1) * H >= (3 * W + 1) * H0;
                    b02 = (W - 1) * H <= (3 * W - 1) * H0;
                    if (!b01) D[H0] = W * H0 - (W - 1) / 2 * (H - H0);
                    else if (!b02) D[H0] = (W + 1) / 2 * (H - H0) - W * H0;
                    else D[H0] = H - H0;
                }
            }
            rl = D.Min();
            HKJ:
            int R = rl < int.MaxValue ? (int)rl : int.MaxValue;
            if (Res > R) Res = R;
            //Hor and Ver
            int K = W;W = H;H = K;
            D = new long[H];
            D[0] = long.MaxValue;
            even = W % 2 == 0;
            if (even)
            {
                rl = Math.Min(-W * (H / 3) + (H - H / 3) * (W / 2), W * (H / 3 + 1) - (H - H / 3 - 1) * (W / 2));
                goto HKJL;
            }
            else
            {
                bool b01, b02;
                for (int H0 = 1; H0 < H; H0++)
                {
                    b01 = (W + 1) * H >= (3 * W + 1) * H0;
                    b02 = (W - 1) * H <= (3 * W - 1) * H0;
                    if (!b01) D[H0] = W * H0 - (W - 1) / 2 * (H - H0);
                    else if (!b02) D[H0] = (W + 1) / 2 * (H - H0) - W * H0;
                    else D[H0] = H - H0;
                }
            }
            rl = D.Min();
            HKJL:
            R = rl < int.MaxValue ? (int)rl : int.MaxValue;
            if (Res > R) Res = R;
            return Res;
        }
    }
}