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::cmp::min;
use std::io::prelude::*;
use std::io::stdin;
use std::str::FromStr;

fn main() {
    let h: i64 = read();
    let w: i64 = read();

    let mut ans = 1 << 30;
    let half_w = w / 2;
    let half_h = h / 2;

    for i in 0..h + 1 {
        let mut pieces = [i * w, half_w * (h - i), (w - half_w) * (h - i)];
        pieces.sort();
        ans = min(ans, pieces[2] - pieces[0]);
    }

    for i in 0..w + 1 {
        let mut pieces = [i * h, half_h * (w - i), (h - half_h) * (w - i)];
        pieces.sort();
        ans = min(ans, pieces[2] - pieces[0]);
    }

    let h1 = h / 3;
    let h2 = (h - h1) / 2;
    let h3 = h - h2 - h1;
    let mut array = [h1, h2, h3];
    array.sort();
    ans = min(ans, (array[2] - array[0]) * w);

    let w1 = w / 3;
    let w2 = (w - w1) / 2;
    let w3 = w - w2 - w1;
    let mut array = [w1, w2, w3];
    array.sort();
    ans = min(ans, (array[2] - array[0]) * h);

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

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