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: Wrong Answer)

#[allow(unused_macros)]
macro_rules! get {
    ([$t:ty] ; $n:expr) => {
        (0..$n)
        .map(|_| get!([$t])).collect::<Vec<_>>()
    };
    ($($t:ty),+ ; $n:expr) => {
        (0..$n).map(|_| get!($($t),+)).collect::<Vec<_>>()
    };
    ([$t:ty]) => {
        rl().split_whitespace()
        .map(|x| x.parse().unwrap())
        .collect::<Vec<$t>>()
    };
    ($t:ty) => {
        rl().parse::<$t>().unwrap()
    };
    ($($t:ty),*) => {
        {
            let line =rl();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap()),*)
        }
    };
}
fn rl() -> String {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    line.trim().to_string()
}

fn main() {
    let (h, w) = get!(i64, i64);
    if h % 3 == 0 || w % 3 == 0 {
        println!("0");
        return;
    }

    let mut aw = 1 << 60;
    for i in 1..w {
        let s1 = i * h;
        let rest = w * h - s1;
        let s2 = rest - ((w - i) * (h / 2));
        let s3 = rest - s2;
        assert! {0 <= s1};
        assert! { 0 <= s2};
        assert! { 0 <= s3};
        let mut v = vec![s1, s2, s3];
        v.sort();
        aw = std::cmp::min(aw, v[2] - v[0]);
    }
    let mut ah = 1 << 60;
    for i in 1..h {
        let s1 = i * w;
        let rest = w * h - s1;
        let s2 = rest - ((h - i) * (w / 2));
        let s3 = rest - s2;
        assert! {0 <= s1};
        assert! { 0 <= s2};
        assert! { 0 <= s3};
        let mut v = vec![s1, s2, s3];
        v.sort();
        ah = std::cmp::min(ah, v[2] - v[0]);
    }
    println!("{}", std::cmp::min(aw, ah));
}