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 provides
//
// File:  c.go
// Author: ymiyamoto
//
// Created on Thu Jan 17 15:56:11 2019
//
package main

import (
	"fmt"
	"sort"
)

var H, W int

func max(slice ...int) int {
	sort.Ints(slice)
	return slice[len(slice)-1]
}

func min(slice ...int) int {
	sort.Ints(slice)
	return slice[0]
}

func minDiffArea(a, b, c int) int {
	return max(a, b, c) - min(a, b, c)
}

func splitH() int {
	arr := make([]int, H-1)
	for h := range arr {
		a := (h + 1) * W
		b := (H - (h + 1)) / 2 * W
		c := H*W - a - b
		arr[h] = minDiffArea(a, b, c)
	}
	return min(arr...)
}

func splitV() int {
	arr := make([]int, W-1)
	for w := range arr {
		a := (w + 1) * W
		b := (H - (w + 1)) / 2 * W
		c := H*W - a - b
		arr[w] = minDiffArea(a, b, c)
	}
	return min(arr...)
}

func splitHV() int {
	arr := make([]int, H-1)
	for h := range arr {
		a := (H - h - 1) * W
		b := (h + 1) * (W / 2)
		c := H*W - a - b
		arr[h] = minDiffArea(a, b, c)
	}
	return min(arr...)
}

func splitVH() int {
	arr := make([]int, W-1)
	for w := range arr {
		a := (W - w - 1) * H
		b := (w + 1) * (H / 2)
		c := H*W - a - b
		arr[w] = minDiffArea(a, b, c)
	}

	return min(arr...)
}

func main() {
	fmt.Scan(&H, &W)

	fmt.Println(min(splitH(), splitHV(), splitV(), splitVH()))
}