Mysterious Light

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 #define ll long long
 4 int main()
 5 {
 6     ll i,j,k,m,n,x;
 7     ll sum;
 8     ll a,b;
 9     int flag=1;
10     cin>>n>>x;
11     a=x,b=n-x;
12     sum=n;
13     while(flag)
14     {
15         if(a>b)
16         {
17             ll y=a/b;
18             if(a%b==0)
19                 y--;
20             a=a-y*b;
21             sum+=2*y*b;
22         }
23         else if(a<b)
24         {
25             ll y=b/a;
26             if(b%a==0)
27                 y--;
28             b=b-y*a;
29             sum+=2*y*a;
30         }
31         else
32         {
33             sum+=a;
34             flag=0;
35         }
36     }
37     cout<<sum<<endl;
38     return 0;
39 }

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≦10¹²
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.

The input is given from Standard Input in the following format:N X

Print the total length of the ray‘s trajectory.

5 2

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.

就是一个不停减转化为除的过程。