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 Perl (v5.18.2) (judge verdict: Wrong Answer)

#!/usr/bin/perl
use Math::BigInt;

while (<>) {
    ($n, $x) = split /\s/, $_;
    last;
}

$d = Math::BigInt->new($n);

if ($x <= $n / 3) {
    $d =  ($n - $x) * 3;
} elsif ($n / 3 < $x && $x < $n / 2) {
    $d = ($n - $x) * 4;
} elsif ($n / 2 == $x) {
    $d =  $x * 3;
} elsif ($n / 2 < $x && $x < ($n * 2) / 3) {
    $d = ($n - $x) * 2 * 3;
} else {
    $d = $x * 3;
}

print "$d\n";