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::BufRead;
fn main() {
    let stdin = std::io::stdin();
    let line = stdin.lock().lines().next().unwrap().unwrap();
    let mut split = line.split(' ').map(|x| x.parse::<u64>().unwrap());
    let (n, mut x) = (split.next().unwrap(), split.next().unwrap());

    if x * 2 == n {
        println!("{}", x * 3);
        std::process::exit(0);
    }

    // The resulting parallelogram is the same.
    if x > n / 2 {
        x = n - x;
    }
    let mut dist = n;
    // Starting from an obtuse angle.  a is the longer edge.
    let (mut a, mut b) = (n - x, x);
    loop {
        let rem = a % b;
        if rem == 0 {
            dist += (a - rem) * 2 - b;
            break;
        }
        dist += (a - rem) * 2;
        a = b;
        b = rem;
    }
    println!("{}", dist);
}