Mysterious Light

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.

btriangle.png

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.

Input

The input is given from Standard Input in the following format:

N X

Output

Print the total length of the ray's trajectory.

Example

Input

5 2

Output

12

inputFormat

Input

The input is given from Standard Input in the following format:

N X

outputFormat

Output

Print the total length of the ray's trajectory.

Example

Input

5 2

Output

12

样例

5 2

12