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>) {
    abc062c()
}

fun abc062c() {
    val (h, w) = readLine()!!.split(" ").map { it.toLong() }

    // h or wが3の倍数の場合は直線に三分割
    if (h % 3L == 0L || w % 3L == 0L) {
        println(0)
        return
    }

    val minDiffOfAll = Math.min(calcAnswer(h, w), calcAnswer(w, h))

    println(minDiffOfAll)
}

private fun calcAnswer(h: Long, w: Long): Long {
    var minDiffOfAll = Long.MAX_VALUE
    for (i in 1 until h) {
        val piece1 = i * w
        val remainHeight = h - i
        // 横の字に切るパターン
        val pieceH = (remainHeight / 2) * w
        val pieceHLarger = if (remainHeight % 2L == 0L) pieceH else (remainHeight / 2 + 1) * w
        val maxPieceH = Math.max(piece1, pieceHLarger)
        val minPieceH = Math.min(piece1, pieceH)
        val diffH = maxPieceH - minPieceH
        // 横/Tの字に切るパターン
        val pieceV = remainHeight * (w / 2)
        val pieceVLarger = if (w % 2L == 0L) pieceV else remainHeight * (w / 2 + 1)
        val maxPieceV = Math.max(piece1, pieceVLarger)
        val minPieceV = Math.min(piece1, pieceV)
        val diffV = maxPieceV - minPieceV

        val minDiff = Math.min(diffH, diffV)
        if (minDiff < minDiffOfAll) minDiffOfAll = minDiff
    }
    return minDiffOfAll
}