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.Linq;
using System.Collections.Generic;

namespace AtCoder
{
	class MainClass
	{
		public static void Main (string[] args)
		{
			var x = Console.ReadLine ().Split (' ').Select(long.Parse).ToArray ();
			var ans = Ans (x);
			x = new[]{ x [1], x [0] };
			ans = Math.Min (ans, Ans (x));
			Console.WriteLine (ans);
		}
		static long Ans(long[] x)
		{
			var area = new long[3];
			var result = long.MaxValue;
			if (x [0] % 3 == 0 || x [1] % 3 == 0) return 0;
			else {
				for (int i = 0; i< x[0]+1; i++) {
					area[0] = i*x[1];
					area[1] = (x[0]-i)*(x [0]/2);
					area [2] = x[0]*x[1]-area[0]-area[1];
					var hoge = Max (area) - min (area);
					if (hoge < result)
						result = hoge;
					area[1] = (x[0]-i)*(x [1]/2);
					area [2] = x[0]*x[1]-area[0]-area[1];
					hoge = Max (area) - min (area);
					if (hoge < result)
						result = hoge;
				}
			}
			return result;
		}
		public static long Max(long[] a)
		{
			long max = a[0];
			for (int i = 1; i < a.Length; i++) {
				if (a [i] > max)
					max = a [i];
			}
			return max;
		}
		public static long min(long[] a)
		{
			long min= (int)a[0];
			for (int i = 1; i < a.Length; i++) {
				if (a [i] < min)
					min = a [i];
			}
			return min;
		}
	}
}