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 Bar
{
	static public void Main(string[] args)
	{
		int H, W;
		string[] vals = Console.ReadLine().Split(' ');
		H = int.Parse(vals[0]);
		W = int.Parse(vals[1]);
		long min1 = calcMin(H,W);
		long min2 = calcMin(W,H);
		Console.WriteLine(Math.Min(min1, min2));
	}
	
	static long calcMin(long H, long W)
	{
		long min = long.MaxValue;

		for(long h=1; h<=H-1; h++)
		{
			long SA, SB, SC;
			SA = h * W;

			long h2 = (H-h) / 2;
			long h3 = H - h - h2;
			//Console.WriteLine("h={0}, h2={1}, h3={2}", h, h2, h3);
			if(h2 > 0 && h3 > 0)
			{
				SB = h2 * W;
				SC = h3 * W;
				long[] S = {SA,SB,SC};
				Array.Sort(S);
				long d = S[2] - S[0];
				if(d >= 0 && d < min)
				{
					//Console.WriteLine("min={0}", d);
					//Console.WriteLine("h={0}, h2={1}, h3={2}", h, h2, h3);
					min = d;
				}
			}

			long w = W / 2;
			long w2 = W - w;
			if(w > 0 && w2 > 0)
			{
				SB = (H-h) * w;
				SC = (H-h) * w2;
				long[] S = {SA,SB,SC};
				Array.Sort(S);
				long d = S[2] - S[0];
				if(d >= 0 && d < min)
				{
					//Console.WriteLine("min={0}", d);
					//Console.WriteLine("h={0}, w={1}, w2={2}", h, w, w2);
					min = d;
				}
			}
		}

		return min;
	}
}