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_macros)]
macro_rules! scan {
    () => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.trim().to_string()
        }
    };
    (;;$n:expr) => {
        (0..$n).map(|_| scan!()).collect::<Vec<_>>()
    };
    ($t:ty) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t:ty),*) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            (
                $(iter.next().unwrap().parse::<$t>().unwrap(),)*
            )
        }
    };
    ($t:ty;;) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.split_whitespace()
                .map(|t| t.parse::<$t>().unwrap())
                .collect::<Vec<_>>()
        }
    };
    ($t:ty;;$n:expr) => {
        (0..$n).map(|_| scan!($t;;)).collect::<Vec<_>>()
    };
    ($t:ty; $n:expr) => {
        (0..$n).map(|_|
                    scan!($t)
        ).collect::<Vec<_>>()
    };
    ($($t:ty),*; $n:expr) => {
        (0..$n).map(|_|
                    scan!($($t),*)
        ).collect::<Vec<_>>()
    };
}

fn main() {
    let (h, w) = scan!(i64, i64);
    let v1 = (1..h)
        .map(|i| {
            let v = vec![i * w, (h - i) / 2 * w, (h - i - (h - i) / 2) * w];
            v.iter().max().unwrap() - v.iter().min().unwrap()
        })
        .min()
        .unwrap();

    let v2 = (1..w)
        .map(|i| {
            let v = vec![i * h, (w - i) / 2 * h, (w - i - (w - i) / 2) * h];
            v.iter().max().unwrap() - v.iter().min().unwrap()
        })
        .min()
        .unwrap();

    let v3 = (1..h)
        .map(|i| {
            let v = vec![i * w, (h - i) * (w / 2), (h - i) * (w - w / 2)];
            v.iter().max().unwrap() - v.iter().min().unwrap()
        })
        .min()
        .unwrap();

    let v4 = (1..w)
        .map(|i| {
            let v = vec![i * h, (w - i) * (h / 2), (w - i) * (h - h / 2)];
            v.iter().max().unwrap() - v.iter().min().unwrap()
        })
        .min()
        .unwrap();

    println!("{}", vec![v1, v2, v3, v4].iter().min().unwrap())
}