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
import math._

object Main extends App {

  val sc = new Scanner(System.in)

  val h, w = sc.nextInt()

  println(min(minimum(h, w), minimum(w, h)))

  def minimum(h: Int, w: Int) : Long = Stream.range(1, h)
    .map(h1 => (h1, (h - h1) / 2, w / 2))
    .map {
      case (h1, h2, w2) => calc(h, w, h1, h2, w2)
    }
    .fold(1L * h * w) {
      case (ans, t) => min(ans, t)
    }

  def calc(h: Int, w: Int, h1 : Long, h2: Long, w2: Long): Long = {
    val s1 = 1L * h1 * w
    val sl2 = 1L * h2 * w
    val sl3 = 1L * (h - h1 - h2) * w
    val sr2 = 1L * (h - h1) * w2
    val sr3 = 1L * (h - h1) * (w - w2)

    var sl = 1L * h * w
    if (sl2 != 0) sl = Seq(s1, sl2, sl3).max - Seq(s1, sl2, sl3).min

    var sr = 1L * h * w
    if (sr2 != 0) sr = Seq(s1, sr2, sr3).max - Seq(s1, sr2, sr3).min

    min(sl, sr)
  }
}