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 Scala (2.11.7) (judge verdict: Accepted)

import java.util.Scanner

object Main extends App {
  val sc = new Scanner(System.in)

  val h = sc.nextLong
  val w = sc.nextLong

  val res =
    if (h % 3 == 0 || w % 3 == 0) 0
    else {
      val l = math.max(h, w)
      val s = math.min(h, w)

      val formT = {
        (1 to (s / 2).toInt).toVector.map { i =>
          val list = List(i * l, (s - i) * (l / 2), (s - i) * (l - l / 2)).sorted
          list.last - list.head
        }
      }.min

      val formTT = {
        (1 to (l / 2).toInt).toVector.map { j =>
          val list = List(j * s, (l - j) * (s / 2), (l - j) * (s - s / 2)).sorted
          list.last - list.head
        }
      }.min

      List(s,formT,formTT).min
    }

  println(res)
}