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;

namespace AtCoderBeginnerContest
{
    public class Program
    {
        static long H;
        static long W;
        static long s;

        public static void Main(string[] args)
        {
            var HW = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();

            if(HW[0]>HW[1])
            {
                H = HW[0];
                W = HW[1];
            }
            else
            {
                H = HW[1];
                W = HW[0];
            }
            s = H * W;

            // ３分割できるとき
            if(H%3== 0 || W%3==0)
            {
                Console.WriteLine(0);
                return;
            }

            // できないとき
            // a1の高さがHのとき（左の四角）
            for (long i = 1; i <= W; i++)
            {
                long a1 = H * i;
                long a2 = (long)(H / 2) * i;
                long a3 = H * W - a1 - a2;
                var sw = Math.Abs(a1 - a2);
                if (sw < Math.Abs(a1 - a3)) sw = Math.Abs(a1 - a3);
                if (sw < Math.Abs(a2 - a3)) sw = Math.Abs(a2 - a3);
                if (s > sw) s = sw;
            }
            for (long i = 1; i <= W; i++)
            {
                long a1 = H * i;
                long a2 = (long)(W / 2) * i;
                long a3 = H * W - a1 - a2;
                var sw = Math.Abs(a1 - a2);
                if (sw < Math.Abs(a1 - a3)) sw = Math.Abs(a1 - a3);
                if (sw < Math.Abs(a2 - a3)) sw = Math.Abs(a2 - a3);
                if (s > sw) s = sw;
            }
            // a2の幅がWのとき（上の四角）
            for (long i = 1; i <= H; i++)
            {
                long a1 = i * (long)(W / 2);
                long a2 = (H-i)*W;
                long a3 = H * W - a1 - a2;
                var sw = Math.Abs(a1 - a2);
                if (sw < Math.Abs(a1 - a3)) sw = Math.Abs(a1 - a3);
                if (sw < Math.Abs(a2 - a3)) sw = Math.Abs(a2 - a3);
                if (s > sw) s = sw;
            }
            for (long i = 1; i <= H; i++)
            {
                long a1 = i * W;
                long a2 = (long)((H - i)/2) * W;
                long a3 = H * W - a1 - a2;
                var sw = Math.Abs(a1 - a2);
                if (sw < Math.Abs(a1 - a3)) sw = Math.Abs(a1 - a3);
                if (sw < Math.Abs(a2 - a3)) sw = Math.Abs(a2 - a3);
                if (s > sw) s = sw;
            }
            Console.WriteLine(s);
        }
    }
}