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;
class Program{
	static void Main(){
		long[] s=Array.ConvertAll(Console.ReadLine().Split(),long.Parse);
		if(s[0]%3==0||s[1]%3==0){Console.WriteLine("{0}",0);}
		else{
			long ans=Math.Min(s[0],s[1]);
			for(long i=s[0]/2;i>0;i--){
				long a=i*s[1],b=(s[0]-i)*(s[1]/2),c=(s[0]-i)*(s[1]-s[1]/2);
				ans=Math.Min(ans,Math.Abs(Math.Min(Math.Min(a,b),c)-Math.Max(Math.Max(a,b),c)));
			}
			for(long i=s[1]/2;i>0;i--){
				long a=i*s[0],b=(s[1]-i)*(s[0]/2),c=(s[1]-i)*(s[0]-s[0]/2);
				ans=Math.Min(ans,Math.Abs(Math.Min(Math.Min(a,b),c)-Math.Max(Math.Max(a,b),c)));
			}
			Console.WriteLine("{0}",ans);
		}
	}
}