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.*;

public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        Scanner sc = new Scanner(System.in);
        long h = sc.nextLong();
        long w = sc.nextLong();
        
        long a = 0;
        long b = 0;
        long c = 0;
        long answer = Long.MAX_VALUE;
        long max, min;

            
            // System.out.println(a + " " + b + " " + c);
        // pattern A
        for (long i = 1; i <= h - 2; i++) {
            a = i * w;
            if ((h - i) % 2 == 0) {
                b = (h - i) / 2 * w;
                c = (h - i) / 2 * w;
            } else {
                b = (h - i) / 2 * w;
                c = ((h - i) / 2 + 1) * w;
            }
            
            max = Math.max(Math.max(a, b), c);
            min = Math.min(Math.min(a, b), c);
            answer = Math.min(answer, max - min);
        }
        
        // pattern B
        for (long i = 1; i <= h - 1; i++) {
            a = i * w;
            if (w % 2 == 0) {
                b = (h - i) * (w / 2);
                c = (h - i) * (w / 2);
            } else {
                b = (h - i) * (w / 2);
                c = (h - i) * (w / 2 + 1);
            }
            
            max = Math.max(Math.max(a, b), c);
            min = Math.min(Math.min(a, b), c);
            answer = Math.min(answer, max - min);
        }
        
        // pattern C
        for (long i = 1; i <= w - 2; i++) {
            a = i * h;
            if ((w - i) % 2 == 0) {
                b = (w - i) / 2 * h;
                c = (w - i) / 2 * h;
            } else {
                b = (w - i) / 2 * h;
                c = ((w - i) / 2 + 1) * h;
            }
            
            max = Math.max(Math.max(a, b), c);
            min = Math.min(Math.min(a, b), c);
            answer = Math.min(answer, max - min);
        }
        
        // pattern D
        for (long i = 1; i <= w - 1; i++) {
            a = i * h;
            if (h % 2 == 0) {
                b = (w - i) * (h / 2);
                c = (w - i) * (h / 2);
            } else {
                b = (w - i) * (h / 2);
                c = (w - i) * (h / 2 + 1);
            }
            
            max = Math.max(Math.max(a, b), c);
            min = Math.min(Math.min(a, b), c);
            answer = Math.min(answer, max - min);
        }
        
        System.out.println(answer);
    }
}