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 (2.13.1) (judge verdict: Accepted)

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val h, w = sc.nextLong()
  if (h % 3 == 0 || w % 3 == 0) {
    println(0)
  } else {
    var ans = h.min(w)
    for (i <- 1 until h.toInt) {
      val a = w * i
      val b = (w/2) * (h-i)
      val c = ((w+1)/2) * (h-i)
      val sMin = a.min(b)
      val sMax = a.max(c)
      ans = ans.min(sMax - sMin)
    }

    for (i <- 1 until w.toInt) {
      val a = h * i
      val b = (h/2) * (w-i)
      val c = ((h+1)/2) * (w-i)
      val sMin = a.min(b)
      val sMax = a.max(c)
      ans = ans.min(sMax - sMin)
    }
    println(ans)
  }
}