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)

import java.math.*

fun main(args: Array<String>) {
    val (H, W) = readInputLine().split(" ").map { it.toLong() }
    
    var ans = Long.MAX_VALUE
    
    // 縦に切るだけの3分割
    for (w in LongRange(W / 3L, W / 3L + if (W % 3L != 0L) 1L else 0L)) {
        val S1 = H * w
        val S2 = H * ((W - w) / 2L)
        val S3 = H * ((W - w) / 2L + if ((W - w) % 2L != 0L) 1L else 0L)
        val max = Math.max(S1, Math.max(S2, S3))
        val min = Math.min(S1, Math.min(S2, S3))
        ans = Math.min(ans, max - min)
    }
    
    // 横に切るだけの3分割
    for(h in LongRange(H / 3L, H / 3L + if (H % 3L != 0L) 1L else 0L)) {
        val S1 = h * W
        val S2 = ((H - h) / 2L) * W
        val S3 = ((H - h) / 2L + if ((H - h) % 2L != 0L) 1L else 0L) * W
        val max = Math.max(S1, Math.max(S2, S3))
        val min = Math.min(S1, Math.min(S2, S3))
        ans = Math.min(ans, max - min)
    }

    // 縦方向に分割した後、残りを横方向に分割
    for(w in LongRange(W / 3L, W / 3L + if (W % 3L != 0L) 1L else 0L)) {
        val S1 = H * w
        val S2 = (H / 2L) * (W - w)
        val S3 = (H / 2L + if (H % 2L != 0L) 1L else 0L) * (W - w)
        val max = Math.max(S1, Math.max(S2, S3))
        val min = Math.min(S1, Math.min(S2, S3))
        ans = Math.min(ans, max - min)
    }

    // 横方向に分割した後、残りを縦方向に分割
    for(h in LongRange(H / 3L, H / 3L + if (H % 3L != 0L) 1L else 0L)) {
        val S1 = h * W
        val S2 = (H - h) * (W / 2L)
        val S3 = (H - h) * (W / 2L + if (W % 2L != 0L) 1L else 0L)
        val max = Math.max(S1, Math.max(S2, S3))
        val min = Math.min(S1, Math.min(S2, S3))
        ans = Math.min(ans, max - min)
    }

    println(ans)
}

fun readInputLine(): String {
    return readLine()!!
}