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 Rust (1.15.1) (judge verdict: Accepted)

//
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
//
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($y: expr),+) => (::std::cmp::max($x, max!( $($y),+)));
}

macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($y: expr),+) => (::std::cmp::min($x, min!( $($y),+)));
}

// solution 
use std::cmp;
#[allow(unused_mut)]
#[allow(non_snake_case)]
fn main() {
    input! {
        H: usize,
        W: usize,
    }

    let h = H / 3;
    let s1 = h * W;
    let w = W / 2;
    let s2 = (H-h) * w;
    let s3 = (H-h) * (W-w);
    let min = cp(std::usize::MAX, s1, s2, s3);

    let h1 = (H-h)/2;
    let s2 = h1 * W;
    let s3 = (H-h-h1)*W;
    let min = cp(min, s1, s2, s3);

    let h = H / 3 + 1;
    let s1 = h * W;
    let w = W / 2;
    let s2 = (H-h) * w;
    let s3 = (H-h) * (W-w);
    let min = cp(min, s1, s2, s3);

    let h1 = (H-h)/2;
    let s2 = h1 * W;
    let s3 = (H-h-h1)*W;
    let min = cp(min, s1, s2, s3);

    let w = W / 3;
    let s1 = w * H;
    let h = H / 2;
    let s2 = (W-w) * h;
    let s3 = (W-w) * (H-h);
    let min = cp(min, s1, s2, s3);

    let w1 = (W-w) / 2;
    let s1 = w * H;
    let s2 = w1 * H;
    let s3 = (W-w-w1)*H;
    let min = cp(min, s1, s2, s3);
    
    let w = W / 3 + 1;
    let s1 = w * H;
    let h = H / 2;
    let s2 = (W-w) * h;
    let s3 = (W-w) * (H-h);
    let min = cp(min, s1, s2, s3);

    let w1 = (W-w) / 2;
    let s1 = w * H;
    let s2 = w1 * H;
    let s3 = (W-w-w1)*H;
    let min = cp(min, s1, s2, s3);

    println!("{}", min);

}

fn cp(min: usize, s1: usize, s2: usize, s3: usize) -> usize {
    cmp::min(min,
             max!(s1, s2, s3) - min!(s1, s2, s3))
}