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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.util.*;


/**
 * Created by Seiya on 2016/10/16.
 */

public class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        long a = scanner.nextLong();
        long b = scanner.nextLong();


        if(a % 3 == 0 || b % 3 == 0){
            System.out.println(0);
            return;
        }

        long ans = 1999999999;
        for (long i = 1L; i <= a; i++) {
            long tempa = b * (a - i);
            long tempb = i * (b / 2);
            long tempc = a * b - tempa - tempb;
            long max = Math.max(tempa, Math.max(tempb, tempc));
            long min = Math.min(tempa, Math.min(tempb, tempc));
            ans = Math.min(ans, max - min);
        }

        long temp = a;
        a = b;
        b = temp;
        for (long i = 1L; i <= a; i++) {
            long tempa = b * (a - i);
            long tempb = i * (b / 2);
            long tempc = a * b - tempa - tempb;
            long max = Math.max(tempa, Math.max(tempb, tempc));
            long min = Math.min(tempa, Math.min(tempb, tempc));
            ans = Math.min(ans, max - min);
        }
        ans = Math.min(ans, ((a - 2 * (a / 3)) * b) - (a / 3) * b);
        ans = Math.min(ans, ((b - 2 * (b / 3)) * a) - (b / 3) * a);




        System.out.println(ans);


    } // mainMethod


} // MainClass