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 ConsoleApp44 {
    class Program {
        static void Main(string[] args) {
            var st = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();

            int H = st[0];
            int W = st[1];

            if (H % 3 == 0 || W % 3 == 0) {
                Console.WriteLine(0);
                return;
            }




            //一回目が横割りの時
            int ans_tate_yoko = 0;
            //一回目が縦割りの時
            int ans_yoko_tate = 0;

            int[] cand = new int[3];

            int ans_tate_tate = 0;
            int ans_yoko_yoko = 0;

            //縦縦に切るとき
            cand[0] = H * (W / 3);
            cand[1] = H * ((W - W / 3) / 2);
            cand[2] = H * (W - W / 3 - (W - W / 3) / 2);

            Array.Sort(cand);
            ans_tate_tate = cand[2] - cand[0];

            //横横に切るとき
            cand[0] = W * (H / 3);
            cand[1] = W * ((H - H / 3) / 2);
            cand[2] = W * (H - H / 3 - (H - H / 3) / 2);

            Array.Sort(cand);
            ans_yoko_yoko = cand[2] - cand[0];

            if (H % 3 == 1) {
                cand[0] = (W / 2) * (H - H / 3);
                cand[1] = (W - W / 2) * (H - H / 3);
                cand[2] = W * (H / 3);

                Array.Sort(cand);

                ans_tate_yoko = cand[2] - cand[0];
            } else if (H % 3 == 2) {
                cand[0] = (W / 2) * (H - H / 3 - 1);
                cand[1] = (W - W / 2) * (H - H / 3 - 1);
                cand[2] = W * (H / 3 + 1);

                Array.Sort(cand);

                ans_tate_yoko = cand[2] - cand[0];
            }

            if (W % 3 == 1) {
                cand[0] = (H / 2) * (W - W / 3);
                cand[1] = (H - H / 2) * (W - W / 3);
                cand[2] = H * (W / 3);

                Array.Sort(cand);

                ans_yoko_tate = cand[2] - cand[0];
            } else if (W % 3 == 2) {
                cand[0] = (H / 2) * (W - W / 3 - 1);
                cand[1] = (H - H / 2) * (W - W / 3 - 1);
                cand[2] = H * (W / 3 + 1);

                Array.Sort(cand);

                ans_yoko_tate = cand[2] - cand[0];
            }


            Console.WriteLine(Math.Min(Math.Min(Math.Min(ans_tate_yoko, ans_yoko_tate), ans_tate_tate), ans_yoko_yoko));
        }
    }
}