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 Ruby (2.3.3) (judge verdict: Wrong Answer)

#! ruby
# Try AtCoder
# author: Leonardone @ NEETSDKASU
############################################################
def gs() gets.chomp end
def gi() gets.to_i end
def gf() gets.to_f end
def gss() gs.split end
def gis() gss.map(&:to_i) end
def nmapf(n,f) n.times.map{ __send__ f } end
def ngs(n) nmapf n,:gs end
def ngi(n) nmapf n,:gi end
def ngss(n) nmapf n,:gss end
def ngis(n) nmapf n,:gis end
def arr2d(h,w,v=0) h.times.map{[v] * w} end
def for2p(hr,wr,&pr) hr.each{|i|wr.each{|j| yield(i,j)}} end
def nsum(n) n * (n + 1) / 2 end
def vcount(d,r=Hash.new(0)) d.inject(r){|r,e| r[e]+=1;r} end
############################################################

n, x = gis

case n <=> x * 2
when 0
    puts x * 3
    
when 1
    y = n - x
    z = n - 2 * x
    puts x * 3 + y + z * (x / z + 1)
    
when -1
    y = n - x
    puts  y + x * (y / x + 1)
    
end