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 AtCoderTest
{
    public class Program
    {
        public static void Main(string[] args)
        {
            string[] s = Console.ReadLine().Split();
            int h = int.Parse(s[0]);
            int w = int.Parse(s[1]);

            if(h % 3 == 0 || w % 3 == 0)
            {
                Console.WriteLine(0);
            }
            else
            {
                int mx = h > w ? h : w;
                int mn = w < h ? w : h;
                int mx_h = mx / 3 + 1;
                int mx_w = mn;
                int d_mx = mx - mx_h;
                int mx1 = d_mx > mx_w ? d_mx : mx_w;
                int mn1 = mx_w < d_mx ? mx_w : d_mx;
                int mn_h = mx1 / 2;
                int mn_w = mn1;
                if(mn1 % 2 == 0)
                {
                    mn_h = mn1 / 2;
                    mn_w = mx1;
                }
                int diff1 = mx_h * mx_w - mn_h * mn_w;

                mx_h = mx / 3;
                mx_w = mn;
                d_mx = mx - mx_h;
                mx1 = d_mx > mx_w ? d_mx : mx_w;
                mn1 = mx_w < d_mx ? mx_w : d_mx;
                mn_h = mx1 / 2;
                mn_w = mn1;
                int mm_h = mn_h + (mx1 % 2);
                int mm_w = mn_w;
                if (mn1 % 2 == 0)
                {
                    mn_h = mn1 / 2;
                    mn_w = mx1;
                    mm_h = mn_h;
                    mm_w = mn_w;
                }
                int diffa = Math.Abs(mx_h * mx_w - mm_h * mm_w);
                int diffb = Math.Abs(mn_h * mn_w - mm_h * mm_w);
                int diff2 = diffa > diffb ? diffa : diffb;

                mx_h = mn / 3 + 1;
                mx_w = mx;
                d_mx = mn - mx_h;
                mx1 = d_mx > mx_w ? d_mx : mx_w;
                mn1 = mx_w < d_mx ? mx_w : d_mx;
                mn_h = mx1 / 2;
                mn_w = mn1;
                if (mn1 % 2 == 0)
                {
                    mn_h = mn1 / 2;
                    mn_w = mx1;
                }
                int diff3 = mx_h * mx_w - mn_h * mn_w;

                mx_h = mn / 3;
                mx_w = mx;
                d_mx = mn - mx_h;
                mx1 = d_mx > mx_w ? d_mx : mx_w;
                mn1 = mx_w < d_mx ? mx_w : d_mx;
                mn_h = mx1 / 2;
                mn_w = mn1;
                mm_h = mn_h + (mx1 % 2);
                mm_w = mn_w;
                if (mn1 % 2 == 0)
                {
                    mn_h = mn1 / 2;
                    mn_w = mx1;
                    mm_h = mn_h;
                    mm_w = mn_w;
                }
                diffa = Math.Abs(mx_h * mx_w - mm_h * mm_w);
                diffb = Math.Abs(mn_h * mn_w - mm_h * mm_w);
                int diff4 = diffa > diffb ? diffa : diffb;

                int diff = new List<int> { diff1, diff2, diff3, diff4 }.Min();
                
                Console.WriteLine(diff);
            }
        }
    }
}