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 Go (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"

const max = 10000000000

const (
	DirectionNone = int64(iota)
	DirectionRight
	DirectionLeft
)

var h, w, size int64

func abs(i int64) int64 {
	if i < 0 {
		return -i
	}
	return i
}

func calcLeft(x int64) int64 {
	return x * h
}

func calcRightUp(x int64) int64 {
	return (w - x) * (h/2 + h%2)
}

func calcRightDown(x int64) int64 {
	return (w - x) * (h / 2)
}

func calcMin(x, min, direction int64) int64 {
	left, rightUp, rightDown := calcLeft(x), calcRightUp(x), calcRightDown(x)

	if direction == DirectionNone {
		if left < rightDown {
			direction = DirectionRight
		} else {
			direction = DirectionLeft
		}
	}

	if abs(rightUp-rightDown) < abs(rightDown-left) {
		diff := abs(left - rightDown)
		if diff < min {
			min = diff
		}
	}

	switch direction {
	case DirectionRight:
		if left > rightDown {
			return min
		}
		return calcMin(x+1, min, direction)
	case DirectionLeft:
		if rightDown > left {
			return min
		}
		return calcMin(x-1, min, direction)
	}
	return -1
}

func main() {
	fmt.Scan(&h, &w)
	size = h * w

	if h%3 == 0 || w%3 == 0 {
		fmt.Println(0)
		return
	}

	if h > w {
		h, w = w, h
	}

	x := w / 3

	fmt.Println(calcMin(x, max, 0))
}