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 ans = (sc.nextInt, sc.nextInt) match {
    case (w, h) if w % 3 == 0 || h % 3 == 0 => 0
    case (w, h) =>
      val init = w min h
      val a = aaa(w, h)
      val b = aaa(h, w)
      init min a min b
  }
  println(ans)

  def aaa(a: Int, b: Int): Int = {
    val xxx = for {
      aa <- List(a / 3, a / 3 + 1)
    } yield {
      val b1 = b / 2
      val b2 = b - b1
      val x1 = aa * b
      val x2 = (a - aa) * b1
      val x3 = (a - aa) * b2
      (x1 max x2 max x3) - (x1 min x2 min x3)
    }
    xxx(0) min xxx(1)
  }
}