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 PHP (5.6.30) (judge verdict: Time Limit Exceeded)

<?php
    /*
        Problem URL : http://agc001.contest.atcoder.jp/tasks/agc001_b

        Score  :
        Result :
        Time   : ms
        Memory : KB
     */

    ini_set('display_errors', 'Off');
    ini_set('error_reporting', E_ALL & ~E_NOTICE);

    fscanf(STDIN, "%d %d", $N, $X);

    $a = $X;
    $b = 0;
    $direction = "b";
    $answer = 0;

    // そこを通ったか
    $m[$a][$b] = -1;
    // 航跡
    $n[$a][$b] = "";

    while($m[$X][0] < 0) {
        switch($direction) {
            case "a":
                $a++;
                $answer++;
                break;

            case "b":
                $b++;
                $answer++;
                break;

            case "-ab":
                $a--;
                $b--;
                $answer++;
                break;

        }
        // echo "{$direction} a:{$a} b:{$b} ans:{$answer}\n";

        // インクリメント
        $m[$a][$b]++;
        // 右の壁にぶつかった
        if ($a == $b) {
            $direction = "a";
        }
        // 下の壁にぶつかった
        elseif ($a == $N) {
            $direction = "-ab";
        }
        // 左の壁にぶつかった
        elseif ($b == 0) {
            $direction = "b";
        }
        // すでに航跡がある
        elseif ($m[$a][$b] > 0) {
            // echo "aru {$n[$a][$b]}\n\n";
            if ($direction == "b" && $n[$a][$b] == "a") {
                $direction = "-ab";
            }
            elseif ($direction == "b" && $n[$a][$b] == "-ab") {
                $direction = "a";
            }
            elseif ($direction == "-ab" && $n[$a][$b] == "b") {
                $direction = "a";
            }
            elseif ($direction == "-ab" && $n[$a][$b] == "a") {
                $direction = "b";
            }
            elseif ($direction == "a" && $n[$a][$b] == "b") {
                $direction = "-ab";
            }
            elseif ($direction == "a" && $n[$a][$b] == "-ab") {
                $direction = "b";
            }
        }
        $n[$a][$b] = $direction;
    }
    // echo "direct:{$direction}\n";
    // echo "ENDE\n";

    echo $answer . "\n";