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(dead_code)]
mod scanner {
    use std::io::StdinLock;
    use std::str::FromStr;
    use std::io::BufRead;
    pub struct Scanner<'a> {
        stdin: StdinLock<'a>,
        token: Vec<String>,
    }
    impl<'a> Scanner<'a> {
        pub fn new(stdin: StdinLock) -> Scanner {
            Scanner {
                stdin: stdin,
                token: vec![],
            }
        }
        pub fn read<T: FromStr>(&mut self) -> T {
            loop {
                if let Some(token) = self.token.pop() {
                    return token.parse().ok().expect("Scanner : Parse Error");
                }
                let mut s = String::new();
                self.stdin.read_line(&mut s).unwrap();
                self.token = s.trim().split_whitespace().rev().map(String::from).collect();
            }
        }
    }
}

fn main() {
    let stdin = std::io::stdin();
    let sc = scanner::Scanner::new(stdin.lock());
    run(sc);
}

use std::cmp::{min, max};

fn run(mut sc: scanner::Scanner) {
    let h: i64 = sc.read();
    let w: i64 = sc.read();
    if h % 3 == 0 || w % 3 == 0 {
        println!("0");
        return;
    }
    let mut ans = min(h, w);
    for &(h, w) in [(h, w), (w, h)].iter() {
        for i in 1..h {
            let a = w * i;
            let b = (w / 2) * (h - i);
            let c = h * w - a - b;
            ans = min(ans, max(a, max(b, c)) - min(a, min(b, c)));
        }
    }
    println!("{}", ans);
}