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.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		string[] input = Console.ReadLine().Split(' ');//Splitで区切り文字を指定して複数個受け取る。
		long h = long.Parse(input[0]);
		long w = long.Parse(input[1]);
		long answer = long.MaxValue;

    if(h % 3 == 0) answer = 0;
    else answer = Math.Min(answer, w);

    if(w % 3 == 0) answer = 0;
    else answer = Math.Min(answer, h);

    for(long i = 1; i < w; i++)
    {
      if(h % 2 == 0)
      {
        answer = Math.Min(answer, Math.Abs(h*i - (h/2)*(w-i)));
      }else
      {
        answer = Math.Min(answer, 
        Math.Max(Math.Abs(h*i - (h/2)*(w-i)), Math.Abs(h*i - (h/2+1)*(w-i))));
      }
    }

    for(long i = 1; i < h; i++)
    {
      if(w % 2 == 0)
      {
        answer = Math.Min(answer, Math.Abs(w*i - (w/2)*(h-i)));
      }else
      {
        answer = Math.Min(answer, 
        Math.Max(Math.Abs(w*i - (w/2)*(h-i)), Math.Abs(w*i - (w/2+1)*(h-i))));
      }
    }
    
		Console.WriteLine(answer);
	}
}