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! parse_line {
    ( $t:ty ) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            iter.next().unwrap().parse::<$t>().unwrap()
        }
    );

    ( $( $t:ty), +) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ( $(iter.next().unwrap().parse::<$t>().unwrap()),* )
        }
    );
}

#[allow(unused_macros)]
macro_rules! read_line {
    () => {{
        let mut line = String::new();
        ::std::io::stdin().read_line(&mut line).unwrap();
        line.pop();
        line
    }};
}

#[allow(unused_macros)]
macro_rules! parse_vec {
    ( $t:ty ) => {{
        let mut line = String::new();
        ::std::io::stdin().read_line(&mut line).unwrap();
        let iter = line.split_whitespace();
        iter.map(|v| v.parse::<$t>().unwrap()).collect::<Vec<_>>()
    }};
}

use std::cmp::min;

fn solve_(h: usize, w: usize) -> usize {
    let mut ans = std::usize::MAX;

    for i in 1..h {
        {
            let mut ss = Vec::new();
            ss.push(i * w);
            ss.push((h - i) * (w / 2));
            ss.push((h - i) * (w / 2 + if w % 2 == 0 { 0 } else { 1 }));
            ss.sort();
            let s = ss[2] - ss[0];
            if s < ans {
                ans = s;
            }
        }

        {
            if h - i < 2 {
                continue;
            }
            let mut ss = Vec::new();
            ss.push(i * w);
            ss.push((h - i) / 2 * w);
            ss.push(((h - i) / 2 + if (h - i) % 2 == 0 { 0 } else { 1 }) * w);
            ss.sort();
            let s = ss[2] - ss[0];
            if s < ans {
                ans = s;
            }
        }
    }
    ans
}

fn solve(h: usize, w: usize) -> usize {
    min(solve_(h, w), solve_(w, h))
}

fn main() {
    let (h, w) = parse_line!(usize, usize);

    println!("{}", solve(h, w));
}

#[test]
fn solve_test() {
    assert_eq!(solve(3, 5), 0);
    assert_eq!(solve(4, 5), 2);
    assert_eq!(solve(5, 5), 4);
    assert_eq!(solve(100000, 2), 1);
    assert_eq!(solve(100000, 100000), 50000);
}