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: Wrong Answer)

#![allow(non_snake_case)]
#![allow(dead_code)]
#![allow(unused_macros)]
#![allow(unused_imports)]

use std::str::FromStr;
use std::io::*;
use std::collections::*;
use std::cmp::*;

struct Scanner<I: Iterator<Item = char>> {
    iter: std::iter::Peekable<I>,
}

macro_rules! exit {
    () => {{
        exit!(0)
    }};
    ($code:expr) => {{
        if cfg!(local) {
            writeln!(std::io::stderr(), "===== Terminated =====")
                .expect("failed printing to stderr");
        }
        std::process::exit($code);
    }}
}

impl<I: Iterator<Item = char>> Scanner<I> {
    pub fn new(iter: I) -> Scanner<I> {
        Scanner {
            iter: iter.peekable(),
        }
    }

    pub fn safe_get_token(&mut self) -> Option<String> {
        let token = self.iter
            .by_ref()
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        if token.is_empty() {
            None
        } else {
            Some(token)
        }
    }

    pub fn token(&mut self) -> String {
        self.safe_get_token().unwrap_or_else(|| exit!())
    }

    pub fn get<T: FromStr>(&mut self) -> T {
        self.token().parse::<T>().unwrap_or_else(|_| exit!())
    }

    pub fn vec<T: FromStr>(&mut self, len: usize) -> Vec<T> {
        (0..len).map(|_| self.get()).collect()
    }

    pub fn mat<T: FromStr>(&mut self, row: usize, col: usize) -> Vec<Vec<T>> {
        (0..row).map(|_| self.vec(col)).collect()
    }

    pub fn char(&mut self) -> char {
        self.iter.next().unwrap_or_else(|| exit!())
    }

    pub fn chars(&mut self) -> Vec<char> {
        self.get::<String>().chars().collect()
    }

    pub fn mat_chars(&mut self, row: usize) -> Vec<Vec<char>> {
        (0..row).map(|_| self.chars()).collect()
    }

    pub fn line(&mut self) -> String {
        if self.peek().is_some() {
            self.iter
                .by_ref()
                .take_while(|&c| !(c == '\n' || c == '\r'))
                .collect::<String>()
        } else {
            exit!();
        }
    }

    pub fn peek(&mut self) -> Option<&char> {
        self.iter.peek()
    }
}

fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin.bytes().map(|c| c.unwrap() as char));
    let H: usize = sc.get();
    let W: usize = sc.get();
    if H % 3 == 0 || W % 3 == 0 {
        println!("0");
        return;
    }
    let mean = (H * W) / 3;
    // はじめに縦に切る場合
    let mut rest = H * W;
    let mut pieces = vec![0; 3];
    pieces[0] = mean + (H - mean % H);
    rest -= pieces[0];
    if H % 2 == 0 {
        pieces[1] = rest / 2;
        pieces[2] = rest / 2;
    } else {
        let rest_w = rest / H;
        pieces[1] = rest_w * (H / 2);
        pieces[2] = rest_w * ((H+1) / 2);
    }
    pieces.sort();
    let case1 = pieces[2] - pieces[0];
    let mut rest = H * W;
    let mut pieces = vec![0; 3];
    pieces[0] = mean - mean % H;
    rest -= pieces[0];
    if H % 2 == 0 {
        pieces[1] = rest / 2;
        pieces[2] = rest / 2;
    } else {
        let rest_w = rest / H;
        pieces[1] = rest_w * (H / 2);
        pieces[2] = rest_w * ((H+1) / 2);
    }
    pieces.sort();
    let case2 = pieces[2] - pieces[0];
    // はじめに横に切る場合
    let mut rest = H * W;
    let mut pieces = vec![0; 3];
    pieces[0] = mean + (W - mean % W);
    rest -= pieces[0];
    if W % 2 == 0 {
        pieces[1] = rest / 2;
        pieces[2] = rest / 2;
    } else {
        let rest_h = rest / W;
        pieces[1] = rest_h * (W / 2);
        pieces[2] = rest_h * ((W+1) / 2);
    }
    pieces.sort();
    let case3 = pieces[2] - pieces[0];
    let mut rest = H * W;
    let mut pieces = vec![0; 3];
    pieces[0] = mean - mean % W;
    rest -= pieces[0];
    if W % 2 == 0 {
        pieces[1] = rest / 2;
        pieces[2] = rest / 2;
    } else {
        let rest_h = rest / W;
        pieces[1] = rest_h * (W / 2);
        pieces[2] = rest_h * ((W+1) / 2);
    }
    pieces.sort();
    let case4 = pieces[2] - pieces[0];
    let ans = min(min(case1, case2), min(case3, case4));
    println!("{}", ans);
}