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::fmt::Debug;
use std::io;
use std::io::{Read, Stdin};
use std::str;
use std::str::FromStr;
use std::cmp;

fn calc(h: i64, w: i64) -> i64 {
    let mut min: i64 = w;
    for h1 in 1..(h + 1) {
        let s1: i64 = h1 * w;
        let h2: i64 = h - h1;
        let w1: i64 = w / 2;
        let w2: i64 = w - w1;

        let s2: i64 = w1 * h2;
        let s3: i64 = w2 * h2;

        let mut max = cmp::max((s1 - s2).abs(), (s1 - s3).abs());
        max = cmp::max(max, (s2 - s3).abs());

        min = cmp::min(min, max);
    }
    min
}

fn main() {
    let mut sc = Scanner::new();
    let h = sc.parse::<i64>();
    let w = sc.parse::<i64>();
    if h % 3 == 0 || w % 3 == 0 {
        println!("0");
        return;
    }

    let ans = cmp::min(calc(h, w), calc(w, h));
    println!("{}", ans);
}


struct Scanner {
    stdin: Stdin,
    buf: Vec<u8>,
}

impl Scanner {
    fn new() -> Scanner {
        Scanner {
            stdin: io::stdin(),
            buf: Vec::with_capacity(256),
        }
    }

    fn parse<T: FromStr>(&mut self) -> T
        where <T as FromStr>::Err: Debug
    {
        self.buf.clear();
        let mut it = self.stdin.lock().bytes();
        let mut c = it.next().unwrap().unwrap();
        while c == ' ' as u8 || c == '\n' as u8 {
            c = it.next().unwrap().unwrap();
        }
        while !(c == ' ' as u8 || c == '\n' as u8) {
            self.buf.push(c);
            c = it.next().unwrap().unwrap();
        }
        str::from_utf8(&self.buf).unwrap().parse::<T>().unwrap()
    }
}