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
import sys

N,X = map(int,input().split())
ans = 0
oldx = 0

if N > 2 * X:

    ans = N
    N = N - X

elif N == 2 * X:
    ans = 3 * X
    print (ans)
    sys.exit()

else:

    ans = N
    oldx = X
    X = N - X
    N = oldx

while True:

    #print (N,X,ans)

    if N % X == 0:
        ans += ((N // X) * 2 - 1) * X
        break

    else:
        ans += ((N // X) * 2 * X)

        oldx = X
        X = N % X
        N = oldx

    

print (ans)
