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)

use std::io::prelude::*;

fn input<T>() -> T
where
    T: std::str::FromStr,
{
    let stdin = std::io::stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

fn main() {
    let h: usize = input();
    let w: usize = input();

    let mut ans = usize::max_value();
    for i in 1..h {
        let h2 = (h - i) / 2;
        let h3 = h - i - h2;

        let s1 = i * w;
        let s2 = h2 * w;
        let s3 = h3 * w;

        let mx = std::cmp::max(s1, std::cmp::max(s2, s3));
        let mn = std::cmp::min(s1, std::cmp::min(s2, s3));
        ans = std::cmp::min(ans, mx - mn);

        let w2 = w / 2;
        let w3 = w - w2;

        let s1 = i * w;
        let s2 = (h - i) * w2;
        let s3 = (h - i) * w3;

        let mx = std::cmp::max(s1, std::cmp::max(s2, s3));
        let mn = std::cmp::min(s1, std::cmp::min(s2, s3));
        ans = std::cmp::min(ans, mx - mn);
    }

    for i in 1..w {
        let h2 = h / 2;
        let h3 = h - h2;

        let s1 = h * i;
        let s2 = h2 * (w - i);
        let s3 = h3 * (w - i);

        let mx = std::cmp::max(s1, std::cmp::max(s2, s3));
        let mn = std::cmp::min(s1, std::cmp::min(s2, s3));
        ans = std::cmp::min(ans, mx - mn);

        let w2 = (w - i) / 2;
        let w3 = w - i - w2;

        let s1 = h * i;
        let s2 = h * w2;
        let s3 = h * w3;

        let mx = std::cmp::max(s1, std::cmp::max(s2, s3));
        let mn = std::cmp::min(s1, std::cmp::min(s2, s3));
        ans = std::cmp::min(ans, mx - mn);
    }

    println!("{}", ans);
}