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.Text;
using System.Collections.Generic;
using System.Linq;
 
 
class Program {
    static List<long> rep;
    static void Main(string[] args){
        //入力を受け取る
        var HW = Console.ReadLine().Split().Select(a => double.Parse(a)).ToArray();
         var H = HW[0];
         var W = HW[1];
         var ans = long.MaxValue;
         
         //Wを固定し、Hを1/3以上の数に
         var Hmax = (long)Math.Ceiling(H/3);
         var resH = H-Hmax;
         //最小値の横の長さ
         var minW = ((long)W)/2;
         //最大値の面積を求める
         var canx1 = Hmax*W;
         //縦分割の最小値の面積を求める
         var cani1 = minW*resH;
         var can1  = (long)(canx1-cani1);
         //最小値の縦の長さ
         var minH = ((long)resH)/2;
         var cani2 = (long)(minH*W);
         var can2 = (long)(canx1-cani2);
         //縦分割と横分割でどちらが差が小さくなるか
         if(can1 > can2){
             ans = can2;
         }else{
             ans = can1;
         }
         
         //Hを固定し、Wを1/3以上の数に
         var Wmax = (long)Math.Ceiling(W/3);
         var resW = (long)(W-Wmax);
         //最小値の縦の長さ
         minH = ((long)H)/2;
         //最大値の面積を求める
         var canx3 = Wmax*(long)H;
         //横分割の最小値の面積を求める
         var cani3 = minH*resW;
         var can3  = (long)(canx3-cani3);
         if(can3 < ans){
             ans = can3;
         }
         
         //最小値の横の長さ
         minW = ((long)resW)/2;
         var cani4 = (long)(minW*H);
         var can4 = (long)(canx3-cani4);
         
         if(can4 < ans){
             ans = can4;
         }
         
         Console.WriteLine(ans);
       　
    }
    
    
}