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.Linq;
public class Hello{
    public static void Main(){
        var line = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var H = line[0];
        var W = line[1];
        var max = 0;
        var min = 0;
        var temp = 0;
        var temp2 = 0;
        
        if(H % 3 == 0 || W % 3 == 0){
            Console.WriteLine(0);
            return;
        }
        
        if(W >= H){
            temp = W / 2;
            max = H * temp;
            temp2 = H / 2;
            min = (W - temp) * temp2; 
        }else{
            temp = H / 2;
            max = W * temp;
            temp2 = W / 2;
            min = (H - temp) * temp2;
        }
        Console.WriteLine(max - min);
        
    }
}