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: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;

class Main{

	public static long solve(long x,long y){
		long menseki = x * y;
		long s1 = menseki;
		long s2 = 0;
		long s3 = 0;
		long result = 0;
		for(int i = 0;i < x;i++){
			s1 = (x - i) * y;
			s2 = i * (y/2);
			s3 = menseki - s1 - s2;
			long smax = Math.max(s1,s2);
			smax = Math.max(s3,smax);
			long smin = Math.min(s1,s2);
			smin = Math.min(s3,smin);
			if(i == 0){
				result = smax - smin;
			}else{
				result = Math.min(result,smax - smin);
			}
			s2 = (i/2) * y;
			s3 = menseki - s1 - s2;
			smax = Math.max(s1,s2);
			smax = Math.max(s3,smax);
			smin = Math.min(s1,s2);
			smin = Math.min(s3,smin);
			result = Math.min(result,smax - smin);			
		}
		for(int i = 0;i < y;i++){
			s1 = x * (y - i);
			s2 = (x/2) * i;
			s3 = menseki - s1 - s2;
			long smax = Math.max(s1,s2);
			smax = Math.max(s3,smax);
			long smin = Math.min(s1,s2);
			smin = Math.min(s3,smin);
			result = Math.min(result,smax - smin);
			s2 = x * (i/2);
			s3 = menseki - s1 - s2;
			smax = Math.max(s1,s2);
			smax = Math.max(s3,smax);
			smin = Math.min(s1,s2);
			smin = Math.min(s3,smin);
			result = Math.min(result,smax - smin);
		}
		return result;

	}

	public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] input = br.readLine().split(" ");
        long x = Long.parseLong(input[0]);
        long y = Long.parseLong(input[1]);
        System.out.println(solve(x,y));

    }

}