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
def main():
    n,x=map(int,input().split())
    a,b=n-x,x
    if(a<b):
       a,b=b,a
    path_length = calc_path(a,b,n)
    print(path_length)

def  calc_path(a1,b1,c1):
    q , mod=divmod(a1,b1)
    count=0
    if mod==0:
         c2=c1+2*b1*q-b1
         return c2
    else:
        count=count+1
        c2=c1+2*b1*q
        a2=a1-b1*q
        b2=b1
        if(a2<b2):
           a2,b2=b2,a2
        return calc_path(a2,b2,c2)
if __name__=='__main__':
  main()
