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.*;
public class Main{

  public static void main(String[] args){
      Scanner sc = new Scanner(System.in);
      long h = sc.nextLong();
      long w = sc.nextLong();

      long minDiff = calculateArea(h, w, Long.MAX_VALUE);
      minDiff = calculateArea(w, h, minDiff);
      
      System.out.println(minDiff);
  }

  private static long calculateArea(long h, long w, long minDiff) {
      long area1 = 0, area2 = 0, area3 = 0;
      for(long i = 1; i <= (h+1)/2; i++) {
          area1 = i * w;
          area2 = (h - i) * (w / 2);
          area3 = (h - i) * (w - w / 2);
          long diff = Math.max(area1, Math.max(area2, area3)) - Math.min(area1, Math.min(area2, area3));
          minDiff = Math.min(minDiff, diff);
      }
      return minDiff;
  }
}