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::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let mut h = read::<usize>();
    let mut w = read::<usize>();
    let mut ans = h * w;
    for _ in 0..2 {
        {
            let d1 = w / 3;
            let d2 = (w - d1) / 2;
            let d3 = w - d1 - d2;
            ans = std::cmp::min(
                ans,
                h * ([d1, d2, d3].iter().max().unwrap() - [d1, d2, d3].iter().min().unwrap()),
            );
        }
        let d1 = w / 2;
        let d2 = w - d1;
        for i in 1..h {
            let a1 = i * w;
            let a2 = (h - i) * d1;
            let a3 = (h - i) * d2;
            ans = std::cmp::min(
                ans,
                [a1, a2, a3].iter().max().unwrap() - [a1, a2, a3].iter().min().unwrap(),
            );
        }
        std::mem::swap(&mut h, &mut w);
    }
    println!("{}", ans);
}