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.Collections;
using System.Linq.Expressions;

static class Program
{
    static void Main()
    {
        new Magatro().Solve();
    }
}

class Magatro
{
    private long H, W;
    private void Scan()
    {
        var line = Console.ReadLine().Split(' ');
        H = int.Parse(line[0]);
        W = int.Parse(line[1]);
    }

    public void Solve()
    {
        Scan();
        if (H % 3 == 0 || W % 3 == 0)
        {
            Console.WriteLine(0);
            return;
        }
        if (H < W)
        {
            long t = H;
            H = W;
            W = t;
        }
        long ans = int.MaxValue;
        {
            long T = H / 3;
            long min = W * T;
            long max = (H - T) * ((W + 1) / 2);
            ans = Math.Min(ans, max - min);
        }
        {
            long T = (H + 2) / 3;
            long max = W * T;
            long min = (H - T) * (W / 2);
            ans = Math.Min(ans, max - min);
        }
        long tt = H;
        H = W;
        W = tt;
        {
            long T = H / 3;
            long min = W * T;
            long max = (H - T) * ((W + 1) / 2);
            ans = Math.Min(ans, max - min);
        }
        {
            long T = (H + 2) / 3;
            long max = W * T;
            long min = (H - T) * (W / 2);
            ans = Math.Min(ans, max - min);
        }
        Console.WriteLine(ans);
        
    }
}