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 static System.Math;

class Program{
  public static void Main(){

    var input = Console.ReadLine().Split();
    int h = int.Parse(input[0]);
    int w = int.Parse(input[1]);
    
    long a,b,c,s;
    long min = h * w;
    for(int i=1;i<h;i++){
      a = i * w;
      b = (h-i) * (w / 2);
      c = h * w - a - b;
      
      if(c!=0){
        long s1 = Math.Min(a,Math.Min(b,c));
        long s2 = Math.Max(a,Math.Max(b,c));
        s = s2-s1;
        min = Math.Min(s,min);
      }
      
      
      b = (h-i) * (w/2);
      c = h * w - a - b; 
      
      if(c!=0){
        long s1 = Math.Min(a,Math.Min(b,c));
        long s2 = Math.Max(a,Math.Max(b,c));
        s = s2-s1;
        min = Math.Min(s,min);
      }
    }
    
    for(int i=1;i<w;i++){
      a = i * h;
      b = (w-i) * (h / 2);
      c = h * w - a - b;
      
      if(c!=0){
        long s1 = Math.Min(a,Math.Min(b,c));
        long s2 = Math.Max(a,Math.Max(b,c));
        s = s2-s1;
        min = Math.Min(s,min);
      }
      
      b = (w-i) * (h/2);
      c = h * w - a - b; 
      
      if(c!=0){
        long s1 = Math.Min(a,Math.Min(b,c));
        long s2 = Math.Max(a,Math.Max(b,c));
        s = s2-s1;
        min = Math.Min(s,min);
      }
    }
    
    Console.WriteLine(min);
  }
}