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)

fun main(args: Array<String>) {
    val (H, W) = readLine()!!.split(" ").map(String::toInt)
    if (H % 3 == 0 || W % 3 == 0) {
        println(0)
    } else {
        val result = split(H, W, 3)
        println(result.max()!! - result.min()!!)
    }
}

fun split(h: Int, w: Int, n: Int): MutableList<Long> {
    if (n == 1) {
        return mutableListOf(h * w.toLong())
    }
    val a = h * w.toLong() / n.toDouble()
    val b = Math.round(h / n.toDouble()) * w
    val c = h * Math.round(w / n.toDouble())
    if (Math.abs(a - b) < Math.abs(a - c)) {
        val length = Math.round(h / n.toDouble()).toInt()
        val result = split(h - length, w, n - 1)
        result.add(w * length.toLong())
        return result
    } else {
        val length = Math.round(w / n.toDouble()).toInt()
        val result = split(h, w - length, n - 1)
        result.add(h * length.toLong())
        return result
    }
}