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::{max,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 read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}
fn main(){
    let hw = read_vec::<u64>();
    let (h,w) = (hw[0],hw[1]);
    // let h = max(hw[0],hw[1]);
    // let w = min(hw[0],hw[1]);
    if h % 3 == 0 || w % 3 == 0 {
        println!("0");
        return;
    }
    let a1 = solve(h,w);
    let a2 = solve(w,h);
    println!("{}",min(a1,a2));
}
fn solve(h:u64,w:u64)->u64{
    let mut ans = h*w;
    for j in 1..h{
        let g = suqare(j, w);
        let h_diff = h - j;
        let (b,r) = calc(h_diff, w);
        let mut v = vec![g,b,r];
        ans = min(v.iter().max().unwrap() -v.iter().min().unwrap(),ans);
        let (b,r) = calc(w,h_diff);
        let mut v = vec![g,b,r];
        ans = min(v.iter().max().unwrap() -v.iter().min().unwrap(),ans);
    }
    ans
}
fn suqare(x:u64,y:u64)->u64{
    x*y
}
fn calc(h:u64,w:u64) -> (u64,u64){
    if h % 2 == 0 {
        let b = suqare(h /2,w);
        (b,b)
    }else{
        let b = suqare(h/2, w);
        let r = suqare (h- h/2, w);
        (b,r)
    }
}