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

func getScanner(fp *os.File) *bufio.Scanner {
	scanner := bufio.NewScanner(fp)
	scanner.Split(bufio.ScanWords)
	scanner.Buffer(make([]byte, 500001), 500000)
	return scanner
}

func getNextString(scanner *bufio.Scanner) string {
	scanner.Scan()
	return scanner.Text()
}

func getNextInt(scanner *bufio.Scanner) int {
	i, _ := strconv.Atoi(getNextString(scanner))
	return i
}

func main() {
	fp := os.Stdin
	if len(os.Args) > 1 {
		fp, _ = os.Open(os.Args[1])
	}

	scanner := getScanner(fp)
	writer := bufio.NewWriter(os.Stdout)

	h := getNextInt(scanner)
	w := getNextInt(scanner)

	ans := 1 << 30

	whole := w * h

	mm := make([]int, 3)
	for i := 1; i < h; i++ {
		mm[0] = i * w
		mm[1] = (h - i) * (w >> 1)
		mm[2] = whole - mm[0] - mm[1]
		sort.Ints(mm)
		if ans > mm[2]-mm[0] {
			ans = mm[2] - mm[0]
		}
		mm[0] = i * w
		mm[1] = (h - i) / 2 * w
		mm[2] = whole - mm[0] - mm[1]
		sort.Ints(mm)
		if ans > mm[2]-mm[0] {
			ans = mm[2] - mm[0]
		}
	}
	for i := 1; i < w; i++ {
		mm[0] = i * h
		mm[1] = (w - i) * (h >> 1)
		mm[2] = whole - mm[0] - mm[1]
		sort.Ints(mm)
		if ans > mm[2]-mm[0] {
			ans = mm[2] - mm[0]
		}
		mm[0] = i * h
		mm[1] = (w - i) / 2 * h
		mm[2] = whole - mm[0] - mm[1]
		sort.Ints(mm)
		if ans > mm[2]-mm[0] {
			ans = mm[2] - mm[0]
		}
	}

	fmt.Fprintln(writer, ans)
	writer.Flush()
}