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::vec::Vec;
use std::cmp::min;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}

fn main() {
    let (h, w) = {
        let v: Vec<usize> = read_vec();
        (v[0], v[1])
    };

    let mut ans = std::usize::MAX;
    // 縦hに沿って1個目を分割
    for wid in 1..w {
        let mut squares = vec![h * wid];
        if h % 2 == 0 || (w-wid) % 2 == 0 {
            let rest = (h * (w-wid)) / 2;
            squares.push(rest);
            squares.push(rest);
        } else {
            // hを２つに分割
            if h > (w-wid) {
               squares.push((w-wid)*(h/2));
               squares.push((w-wid)*(h/2 + 1));
            } else {
                squares.push(h*((w-wid)/2));
                squares.push(h*((w-wid)/2 + 1));
            }
        }
        squares.sort();
        let M = squares[2];
        let m = squares[0];

        ans = min(ans, M - m);
    }

    // 横wに沿って1個目を分割
    for hig in 1..h {
        let mut squares = vec![hig * w];
        if w % 2 == 0 || (h-hig) % 2 == 0 {
            let rest = ((h-hig) * w) / 2;
            squares.push(rest);
            squares.push(rest);
        } else {
            // wを２つに分割
            if w > (h-hig) {
               squares.push((w/2)*(h-hig));
               squares.push((w/2 + 1)*(h-hig));
            } else {
                squares.push(w*((h-hig)/2));
                squares.push(w*((h-hig)/2 + 1));
            }
        }
        squares.sort();
        let M = squares[2];
        let m = squares[0];

        ans = min(ans, M - m);
    }

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