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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let v = read_vec::<i64>();
    let (h, w) = (v[0], v[1]);
    let mut ans = std::i64::MAX;

    for &(h, w) in &[(h, w), (w, h)] {
        let h1 = h / 3;
        let h2 = h - h1 * 2;
        ans = min(ans, (h2 - h1).abs() * w);
    }
    for &(h, w) in &[(h, w), (w, h)] {
        let h1 = (h + 1) / 3;
        let h2 = h - h1 * 2;
        if h2 >= 0 {
            ans = min(ans, (h2 - h1).abs() * w);
        }
    }
    for &(h, w) in &[(h, w), (w, h)] {
        let w1 = w / 2;
        let w2 = w - w1;
        for h1 in 0..h + 1 {
            let h2 = h - h1;
            let area1 = h1 * w;
            let area2 = h2 * w1;
            let area3 = h2 * w2;
            ans = min(
                ans,
                [area1, area2, area3].iter().max().unwrap()
                    - [area1, area2, area3].iter().min().unwrap(),
            );
        }
    }
    println!("{:?}", ans);
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}