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 Scala (2.11.7) (judge verdict: Accepted)

object Main extends App {

	var Array(n, x) = scala.io.StdIn.readLine.split(" ").map(_.toLong)
	
	var x1 = x
	var y1 = n - x

	var flag = true
	var ans = n
	
	while(flag){
		if(x1 > y1){
			val tp = x1
			x1 = y1
			y1 = tp
		}

		if(y1%x1 == 0){
			ans += x1 * ( 2* (y1 / x1) - 1)
			flag = false
		}else{
			ans += x1 * 2 * (y1 / x1)
			y1 = y1 % x1
		}
	}

	println(ans)

}