Problem:
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.

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

//#define DEBUG

long long dist(long long M, long long N) {
	long long D;
	if (N==0) {
#ifdef DEBUG
		printf("\n");
#endif
		return 0;
	}
/*	if (M<N) {
		D = M;
		M = N;
		N = D;
	}*/
	D = (M/N)*2*N;
	if (M%N==0) D -= 1;
#ifdef DEBUG
	printf("+%lld", D);
#endif
	return D+dist(N,M%N);
}

int main() {
	long long L, N, P, X;
	scanf("%lld%lld", &N, &X);
	if (2*X < N) {
#ifdef DEBUG
		printf("%lld+%lld+%lld",X,N-X,X);
#endif
		L = X + (N-X) + X;
		P = N-2*X;
		if (P<X) {
#ifdef DEBUG
			printf("+%lld",X);
#endif
			L += X+dist(X,P);
		} else if (P==X) {
#ifdef DEBUG
			printf("+%lld+%lld",X,X);
#endif
			L += 2*X;
		} else {
#ifdef DEBUG
			printf("+%lld",X);
#endif
			L += X+dist(P,X);
		}
	} else if (2*X == N) {
		L = 3 * X;
	} else {
		L = X;
		L += (N-X) + dist(X,N-X);
	}

	printf("%lld\n", L);
	return 0;
}