Problem:
Score : 500 points

Problem Statement

Snuke is conducting an optical experiment using mirrors and his new invention, the rifle of Mysterious Light.

Three mirrors of length N are set so that they form an equilateral triangle.
Let the vertices of the triangle be a, b and c.

Inside the triangle, the rifle is placed at the point p on segment ab such that ap = X.
(The size of the rifle is negligible.)
Now, the rifle is about to fire a ray of Mysterious Light in the direction of bc.

The ray of Mysterious Light will travel in a straight line, and will be reflected by mirrors, in the same ways as "ordinary" light.
There is one major difference, though: it will be also reflected by its own trajectory as if it is a mirror!
When the ray comes back to the rifle, the ray will be absorbed.

The following image shows the ray's trajectory where N = 5 and X = 2.

It can be shown that the ray eventually comes back to the rifle and is absorbed, regardless of the values of N and X.
Find the total length of the ray's trajectory.

Constraints

2≦N≦10^{12}

1≦X≦N-1

N and X are integers.

Partial Points

300 points will be awarded for passing the test set satisfying N≦1000.

Another 200 points will be awarded for passing the test set without additional constraints.

Input

The input is given from Standard Input in the following format:

N X

Output

Print the total length of the ray's trajectory.

Sample Input 1

5 2

Sample Output 1

12

Refer to the image in the Problem Statement section.
The total length of the trajectory is 2+3+2+2+1+1+1 = 12.

Solution in Rust (1.15.1) (judge verdict: Runtime Error)

use std::fmt::Debug;
use std::str::FromStr;
use std::io::*;

fn main() {
    let i = stdin();
    solve(&mut i.lock(), &mut stdout());
}

fn solve(i: &mut BufRead, o: &mut Write) {
    let nx = read_vec::<usize>(i);
    let n = nx[0];
    let x = nx[1];

    fn f(
        l: usize, // 左の長さ
        b: usize, // 下の長さ
    ) -> usize {
        if l == b {
            l
        } else if l > b {
            b * 2 + f(l - b, b)
        } else {
            let b_next = b % l;
            if b_next == 0 {
                ((b / l) * 2 - 1) * l
            } else {
                f(l, b_next)
            }
        }
    }
    writeln!(o, "{}", n + f(n - x, x)).unwrap();
}

fn read_line(i: &mut BufRead) -> String {
    let mut line = String::new();
    i.read_line(&mut line).unwrap();
    line.trim().to_string()
}
fn read_vec<T: FromStr>(i: &mut BufRead) -> Vec<T>
where
    T::Err: Debug,
{
    read_line(i)
        .split(' ')
        .map(|x| x.parse().unwrap())
        .collect()
}