Contest Duration: - (local time) (110 minutes) Back to Home
B - Mysterious Light /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

このように不思議な光を発射した時、不思議な光は必ず発射した点に戻ってくることが証明できます。 このとき、光の軌跡の長さが全体でいくらになるかを求めて下さい。

### 制約

• 2≦N≦10^{12}
• 1≦X≦N-1
• NX はいずれも整数である。

### 部分点

• N≦1000 を満たすデータセットに正解した場合は、300 点が与えられる。
• 追加制約のないデータセットに正解した場合は、上記とは別に 200 点が与えられる。

### 入力

N X


### 入力例 1

5 2


### 出力例 1

12


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.