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 Java7 (OpenJDK 1.7.0) (judge verdict: Runtime Error)

import java.util.*;
public class Main{
	public static void main(String[] args){
		Scanner stdIn = new Scanner(System.in);
		long N = stdIn.nextInt();
		long X = stdIn.nextInt();
		
		long ans = N;
		
		if(N - X < X){
			ans += square(N - X, X);
		} else{
			ans += square(X, N - X);
		}
		
		System.out.println(ans);
	}
	
	private static long square(long S, long L){
		
		long Q = L/S;
		long R = L%S;
		
		if(R == 0){
			return S*(2*Q - 1);
		} else{
			return S*(2*Q) + square(R, S);
		}
	}
}