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 (1.3.71) (judge verdict: Wrong Answer)

import kotlin.math.max
import kotlin.math.min

fun main(args: Array<String>) {
    Program().solve()
}

class Program {
    fun solve() {
        val sc = MyScanner()
        val h = sc.nextInt()
        val w = sc.nextInt()
        if (h % 3 == 0 || w % 3 == 0) {
            println("0")
            return
        }

        fun calc(a: Long, b: Long, c: Long): Long {
            val min = min(a, min(b, c))
            val max = max(a, max(b, c))
            return max - min
        }

        var ans = Long.MAX_VALUE
        for (w2 in 1 until w) {
            val a = h.toLong() * w2
            val h2 = h / 2
            val b = h2.toLong() * (w - w2)
            val c = (h - h2).toLong() * (w - w2)
            ans = min(ans, calc(a, b, c))
        }

        for (h2 in 1 until h) {
            val a = h2.toLong() * w
            val w2 = w / 2
            val b = (h - h2).toLong() * w2
            val c = (h - h2).toLong() * (w - w2)
            ans = min(ans, calc(a, b, c))
        }

        println(ans)
    }
}

class MyScanner {
    private var ptr = 0
    private var l = listOf<String>()

    fun next(): String {
        while (l.size <= ptr) {
            l = readLine()!!.split(' ')
            ptr = 0
        }
        return l[ptr++]
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextDouble() = next().toDouble()
    fun nextCharArray() = next().toCharArray()
    fun nextChar() = next()[0]

    fun list(): List<String> {
        ptr = l.size
        return readLine()!!.split(' ')
    }

    fun intList() = list().map { s -> s.toInt() }
    fun longList() = list().map { s -> s.toLong() }
    fun doubleList() = list().map { s -> s.toDouble() }

    fun array() = list().toTypedArray()
    fun intArray() = intList().toIntArray()
    fun longArray() = longList().toLongArray()
    fun doubleArray() = doubleList().toDoubleArray()
}