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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func out(x ...interface{}) {
	//	fmt.Println(x...)
}

var sc = bufio.NewScanner(os.Stdin)

func getInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func getString() string {
	sc.Scan()
	return sc.Text()
}

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

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

func main() {
	sc.Split(bufio.ScanWords)

	H, W := getInt(), getInt()
	total := H * W

	// select 1
	n := (H*W + 2) / 3

	x := (n + W - 1) / W
	y := (n + H - 1) / H
	xx := x * W
	yy := y * H

	out("xx,yy", xx, yy, n, x, y)
	if xx < yy {
		H -= x
	} else {
		W -= y
	}

	sel0 := min(xx, yy)

	out(sel0, W, H)

	// select 2
	n = H * W / 2

	x = (n + W - 1) / W
	y = (n + H - 1) / H
	xx = x * W
	yy = y * H
	if xx < yy {
		W -= x
	} else {
		H -= y
	}

	sel1 := min(xx, yy)
	sel2 := total - sel0 - sel1

	out(sel0, sel1, sel2)

	mi := min(sel0, min(sel1, sel2))
	ma := max(sel0, max(sel1, sel2))
	fmt.Println(ma - mi)
}