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)

macro_rules! input {
    ($ttype:ty) => {
        {
            let mut input = String::new();
            let _= std::io::stdin().read_line(&mut input);
            input.trim().parse::<$ttype>().unwrap()
        }
    };

    ($($ttype:ty),*) => {
        {
            use std::io::BufRead;
            let mut input = String::new();
            let stdin = std::io::stdin();
            let _ = stdin.lock().read_line(&mut input);
            let mut iter = input.trim().split_whitespace();
            (
                $(iter.next().unwrap().parse::<$ttype>().unwrap(),)*
            )
        }
    };

    ($ttype:ty; $x:expr) => {
        {
            use std::io::BufRead;
            let mut input = String::new();
            let stdin = std::io::stdin();
            let _ = stdin.lock().read_line(&mut input);
            let v: Vec<$ttype> = input
                .trim()
                .split_whitespace()
                .map(|x| x.parse().unwrap())
                .collect();
            v
        }
    };

    ($ttype:ty; $x:expr; $y:expr) => {
        {
            use std::io::BufRead;
            let mut matrix = Vec::with_capacity($y);
            for _ in 0..$y {
                let mut input = String::new();
                let stdin = std::io::stdin();
                let _ = stdin.lock().read_line(&mut input);
                let v: Vec<$ttype> = input
                    .trim()
                    .split_whitespace()
                    .map(|x| x.parse().unwrap())
                    .collect();
                matrix.push(v);
            }
            matrix
        }
    };
}

fn solve(h: i64, w: i64) -> i64 {
    let mut delta = i64::max_value();
    for ah in 1..h {
        let bh = (h - ah) / 2;
        let ch = h - (ah + bh);
        let mut rectangles = vec![ah * w, bh * w, ch * w];
        rectangles.sort();
        if delta > rectangles[2] - rectangles[0] {
            delta = rectangles[2] - rectangles[0];
        }

        let bh = h - ah;
        let ch = h - ah;
        let bw = w / 2;
        let cw = w - bw;
        let mut rectangles = vec![ah * w, bh * bw, ch * cw];
        rectangles.sort();
        if delta > rectangles[2] - rectangles[0] {
            delta = rectangles[2] - rectangles[0];
        }
    }
    delta
}

fn main() {
    let (h, w) = input!(i64, i64);

    let answer1 = solve(h, w);
    let answer2 = solve(w, h);
    println!("{}", if answer1 > answer2 { answer2 } else { answer1 });
}