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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.util.*

/**
 * Created by zzt on 17-7-7.
 */
fun main(args: Array<String>) {
    val scanner = Scanner(System.`in`)
    val H = scanner.nextInt()
    val W = scanner.nextInt()

    val result = Array(4, { i -> 0 })
    result[0] = ((Math.ceil(H / 3.0) - Math.floor(H / 3.0)) * W).toInt()
    val h = Math.round(H / 3.0)
    result[1] = Math.abs((h * W) - (H - h) * Math.floor(W / 2.0)).toInt()
    result[2] = ((Math.ceil(W / 3.0) - Math.floor(W / 3.0)) * H).toInt()
    val w = Math.round(W / 3.0)
    result[3] = Math.abs((w * H) - (W - w) * Math.floor(H / 2.0)).toInt()

    println(result.sortedArray()[0])
}