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: Wrong Answer)

import scala.io.StdIn
import scala.collection.mutable.ListBuffer

object Main extends App {
  val Array(h, w) = StdIn.readLine.split(" ").map(_.toLong)

  val res1 = {
    val list = ListBuffer.empty[Long]
    val m = h / 2L
    val res = (1L until w)./:(Long.MaxValue, Long.MaxValue)((min, i) => {
      val a =( h * i ) 
      list += a
      list += ( m * (w-i) )
      list += ( (h-m) * (w-i) )
      val r1 = list.max - list.min
      list.clear
      val k = (w-i) / 2L
      list += a
      list += ( k * h )
      list += ( (w-i-k) * h )
      val r2 = list.max - list.min
      list.clear
      ( math.min(min._2, r1), math.min(min._2, r2) )
    })
    math.min(res._1, res._2)
  }

  val res2 = {
    val list = ListBuffer.empty[Long]
    val m = w / 2L
    val res = (1L until h)./:(Long.MaxValue, Long.MaxValue)((min, i) => {
      val a = w * i
      list += a
      list += ( m * (h-i) )
      list += ( (w-m) * (h-i))
      val r1 = list.max - list.min
      list.clear
      val k = (h-i) / 2L
      list += a
      list += ( k * w )
      list += ( (h-i-k) * w )
      val r2 = list.max - list.min
      list.clear
      ( math.min(min._1, r1), math.min(min._2, r2) )
    })
    math.min(res._1, res._2)
  }

  val ans = math.min(res1, res2)
  println(ans)
}