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: Accepted)

package main

import (
	"fmt"
	"sort"
)

func abs(i int) int {
	if i >= 0 {
		return i
	} else {
		return -i
	}
}
func g(a, b, c int) int {
	x := []int{a, b, c}
	sort.Ints(x)
	return x[2] - x[0]
}

func min(a, b int) int {
	if a < b {
		return a
	} else {
		return b
	}
}

func div2(a, h, w int) int {
	if h%2 == 0 || w%2 == 0 {
		return abs(a - h*w/2)
	} else {
		x := h / 2
		b := x * w
		c := (h - x) * w
		d := g(a, b, c)
		x = w / 2
		b, c = x*h, (w-x)*h
		return min(d, g(a, b, c))
	}
}

func main() {
	var h, w int
	fmt.Scan(&h, &w)
	if h%3 == 0 || w%3 == 0 {
		fmt.Println(0)
		return
	}

	ans := 1 << 30
	for a := 1; a < h; a++ {
		b := div2(w*a, h-a, w)
		ans = min(ans, b)
	}
	for a := 1; a < w; a++ {
		b := div2(h*a, h, w-a)
		ans = min(ans, b)
	}
	fmt.Println(ans)
}