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
input = sys.stdin.readline
sys.setrecursionlimit(1000000)
from collections import deque, Counter
def getN():
    return int(input())
def getList():
    return list(map(int, input().split()))
import math
INF = 10**10
def bfs(graph, visited, position, root):
    visited[root] = 1
    position[root] = 0
    deq = deque([root])
    while(deq):
        cur = deq.pop()
        # print(cur)
        for nxt, dist in graph[cur]:
            if position[cur] + dist != position[nxt]:
                if position[nxt] != INF:
                    return False
                else:
                    position[nxt] = position[cur] + dist
            if not visited[nxt]:
                deq.append(nxt)
                visited[nxt] = 1

    return True

def main():
    n,x = getList()

    ans = n
    mx, mn = x, n - x
    if mx < mn:
        mx,mn = mn, mx

    # print(mx, mn)

    while(True):
        if mx % mn == 0:
            ans += 2 * mn * (mx // mn) - mn
            break
        else:
            ans += mn * 2 * (mx // mn)
            mx, mn = mn, mx % mn

    print(ans)


if __name__ == "__main__":

    main()