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 Java7 (OpenJDK 1.7.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {
	public static void main(String []args) {
		Scanner sc = new Scanner(System.in);
		int m = sc.nextInt();
		int n = sc.nextInt();
		Main soln = new Main();
		int[] best = soln.cutter(m, n, 1);
		System.out.println(soln.calcDiv(best));
	}

	private int[] cutter(int mm, int nn, int cnt) {
		int[] res = new int[4-cnt];
		if(cnt==3) {
			res[0] = mm*nn;
			return res;
		}

		int minDiv = mm*nn;
		int[] best = new int[4-cnt];
		for(int p=1; p<=mm/2; p++) {
			res[0] = p*nn;
			int[] temp = cutter(mm-p, nn, cnt+1);
			for(int x=0; x<temp.length; x++) {
				res[x+1] = temp[x];
			}
			int tempDiv = calcDiv(res);
			best = (tempDiv<minDiv)? Arrays.copyOf(res, res.length):best;
			minDiv = (tempDiv<minDiv)? tempDiv:minDiv;
		}
		for(int q=1; q<=nn/2; q++) {
			res[0] = q*mm;
			int[] temp = cutter(mm, nn-q, cnt+1);
			for(int x=0; x<temp.length; x++) {
				res[x+1] = temp[x];
			}
			int tempDiv = calcDiv(res);
			best = (tempDiv<minDiv)? Arrays.copyOf(res, res.length):best;
			minDiv = (tempDiv<minDiv)? tempDiv:minDiv;
		}
		return best;
	}

	private int calcDiv(int[] input) {
		Arrays.sort(input);
		return input[input.length-1] - input[0];
	}
}