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: Accepted)

use std::io::*;

fn calc_lay_length_and_next_wh(w: u64, h: u64) -> ((u64, u64), u64) {
    if w >= h {
        let triangles = w / h;
        let w2 = w % h;
        let h2 = h;

        if w2 == 0 {
            return ((0, 0), h * (2 * triangles - 1));
        } else {
            return ((w2, h2), 2 * h * triangles);
        }
    } else {
        let triangles = h / w;
        let w2 = w;
        let h2 = h % w;

        if h2 == 0 {
            return ((0, 0), w * (2 * triangles - 1));
        } else {
            return ((w2, h2), 2 * w * triangles);
        }
    }
}

fn main() {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();

    let mut itr = buf.split_whitespace();
    let n: u64 = itr.next().unwrap().parse().unwrap();
    let x: u64 = itr.next().unwrap().parse().unwrap();

    let mut w = x;
    let mut h = n - x;
    let mut l = w + h;
    loop {
        let ((w_, h_), l_) = calc_lay_length_and_next_wh(w, h);
        w = w_;
        h = h_;
        l += l_;
        if w == 0 {
            break;
        }
    }

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