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)

n,x = gets.split.map(&:to_i)
m = n.to_f/2
$array = []
$sum = 0
$flg = false

def ab(long,short)
  $array.push(long % short)
  if long % short == 0
    $sum += long*2 - short
    puts $sum
    exit
  else
    $flg = true
    $sum += short * (long/short*2)
    short = long % short
    bc($array[-4],short)
  end
end

def bc(long,short)
  $array.push(long % short)
  if long % short == 0
    if $flg
      $sum += long*2 - short
    else
      $sum += long*2
    end
    puts $sum
    exit
  else
    $flg = true
    $sum += short * (long/short*2)
    ab(short, long % short)
  end
end

$array.push(x)
$array.push(n-x)

if x < m
  $sum += n
  $array.push(x)
  ab(n-x,x)
elsif x == m
  puts x*3
else
  $sum += x
  bc(x,n-x)
end