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)

// Try AtCoder
// author: Leonardone @ NEETSDKASU
package main

import (
	"fmt"
)

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

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

func Abs(a int) int {
	if a < 0 {
		return -a
	} else {
		return a
	}
}

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

	s := h * w

	hh := Max(h, w)
	ww := Min(h, w)

	s3 := s / 3

	yA := s3 / ww

	sA := yA * ww

	xB := ww / 2

	sB := (hh - yA) * xB
	sC := s - sA - sB
	ans1 := Max(Abs(sA-sB), Max(Abs(sB-sC), Abs(sC-sA)))

	k1 := hh / 3
	ans2 := Abs(k1*ww - (hh-2*k1)*ww)

	fmt.Println(Min(ans1, ans2))
}