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>
#include<string.h>
#include<ctype.h>
#include<math.h>

#define FOR(i,a,b) for(i=(a);i<(b);i++)
#define RFOR(i,a,b) for(i=(b);i>=(a);i--)
#define REP(i,n) for(i=0;i<(n);i++)
#define RREP(i,n) for(i=(n)-1;i>=0;i--)
#define MREP(i,n,x) for(i=0;i<(n);i=x)
#define IL() while(1)
#define mLOOP(a,b) while((a)<(b)) 
#define MLOOP(a,b) while((a)>(b))
#define ELOOP(a,b) while((a)==(b))
#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)>(b)?(b):(a))
#define ABS(x) ((x)<0?-1*(x):(x))
#define in scanf
#define out printf
#define ll long long
#define ull unsigned long long
#define int(x) scanf("%d",&x);
#define sint(x,y) scanf("%d %d",&x,&y);
#define lint(x,y) scanf("%d\n%d",&x,&y);
#define char(x) scanf("%c",&x);
#define double(x) scanf("%lf",&x);
#define string(x,n) scanf("%s",x);


int main(){
    ull n,x,i,res=0;
    in("%lld %lld",&n,&x);
    ull tmp = n/x;
    if(n%x==0){
        tmp--;
    }
    res+=(x*3)*tmp;
    out("%lld\n",res);

    return 0;
}