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: Accepted)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        long a[] = new long[2];
        a[0] = in.nextLong();
        a[1] = in.nextLong();

        if (a[0] % 3 == 0 || a[1] % 3 == 0) {
            System.out.println(0);
            return;
        }

        Arrays.sort(a);
        long area = a[0];
        area *= a[1];

        long min = Long.MAX_VALUE;
        for (int i = 1; i < a[1]; i++) {
            long b[] = new long[3];
            b[0] = a[0] * i;
            b[1] = (a[0] / 2) * (a[1] - i);
            b[2] = area - b[0] - b[1];
            Arrays.sort(b);
            min = Math.min(min, b[2] - b[0]);

            long c[] = new long[3];
            c[0] = a[0] * i;
            c[1] = ((a[1] - i) / 2) * a[0];
            c[2] = area - c[0] - c[1];
            Arrays.sort(c);
            min = Math.min(min, c[2] - c[0]);
        }

        long tmp = a[0];
        a[0] = a[1];
        a[1] = tmp;
        for (int i = 1; i < a[1]; i++) {
            long b[] = new long[3];
            b[0] = a[0] * i;
            b[1] = (a[0] / 2) * (a[1] - i);
            b[2] = area - b[0] - b[1];
            Arrays.sort(b);
            min = Math.min(min, b[2] - b[0]);

            long c[] = new long[3];
            c[0] = a[0] * i;
            c[1] = ((a[1] - i) / 2) * a[0];
            c[2] = area - c[0] - c[1];
            Arrays.sort(c);
            min = Math.min(min, c[2] - c[0]);
        }        

        System.out.println(min);
    }
}