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>) {
	var (h, w) = readLine()!!.split(" ").map{ it.toLong() }
	if (h % 3 == 0L || w % 3 == 0L) {
		println(0)
		return
	}
	var ans = Math.min(h, w)
	for (i in 1..(w - 1)) {
		val a = (w - i) * h
		val b = ((h + 1) / 2) * i
		val c = (h / 2) * i
		val diff = Math.max(Math.abs(a - b), Math.max(Math.abs(b - c), Math.abs(c - a)))
		ans = Math.min(ans, diff)
	}
	for (i in 1..(h - 1)) {
		val a = (h - i) * w
		val b = ((w + 1) / 2) * i
		val c = (w / 2) * i
		val diff = Math.max(Math.abs(a - b), Math.max(Math.abs(b - c), Math.abs(c - a)))
		ans = Math.min(ans, diff)
	}
	println(ans)
}