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: Accepted)

fun main(args: Array<String>) {
    val (h, w) = readLine()!!.split(' ').map { it.toLong() }

    fun f(h: Long, w: Long): Long {
        var ans = Long.MAX_VALUE
        for (h1 in 1 until h) {
            val h2 = h - h1

            val a = listOf(h1 * w, (h2 / 2) * w, (h2 - h2 / 2) * w)
            ans = Math.min(ans, a.max()!! - a.min()!!)

            val b = listOf(h1 * w, h2 * (w / 2), h2 * (w - w / 2))
            ans = Math.min(ans, b.max()!! - b.min()!!)
        }
        return ans
    }

    println(Math.min(f(h, w), f(w, h)))
}