Topic link :

Give a coordinate (ex, ey), What points did you come from . The rule of going is x perhaps y Plus their least common multiple lcm(x, y).

consider (ex, ey) It's coming from other places , Let's go to (x,y) When ,gcd(x, y)=k,x=k*m1, y=k*m2.

The next step could be (x, y+x*y/gcd(x, y)) Or is it (x+x*y/gcd(x,y), y).

use k and m1,m2 To express as (k*m1, k*m2+m1*m2*k)=(k*m1, k*m2*(m1+1)), or (k*m1+m1*m2*k, k*m2)=(k*m1*(m2+1), k*m2).

I'll just focus on (k*m1*(m2+1), k*m2).m1 and m2 Mutual quality and (m2+1) And m2 Mutual quality .

that gcd(k*m1*(m2+1), k*m2)=k, That is, no matter what changes , Their greatest common factor is k. It also proves that the path is unique , What we're looking for is the number of possible starting positions , So think about it directly every time x The situation in lega ( namely y>x When , In exchange for x,y). We can (ex, ey) Push it back up .x'=k1*m1/(m2+1), When x No (y + k) After an integral multiple of , namely x/(k*(m2+1)) Not for 0 end .

 #include <algorithm>
#include <iostream>
#include <iomanip>
#include <cstring>
#include <climits>
#include <complex>
#include <fstream>
#include <cassert>
#include <cstdio>
#include <bitset>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <ctime>
#include <set>
#include <map>
#include <cmath> using namespace std; int ex, ey; int main() {
// freopen("in", "r", stdin);
int T, _ = ;
scanf("%d", &T);
while(T--) {
scanf("%d %d", &ex, &ey);
int k = __gcd(ex, ey);
if(ex < ey) swap(ex, ey);
int ans = ;
while() {
if(ex % (ey + k) != ) break;
ex = ex / (ey / k + );
if(ex < ey) swap(ex, ey);
k = __gcd(ex, ey);
printf("Case #%d: %d\n", _++, ans);
return ;

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