1 #include<cstdio>
 2 #include<cstdlib>
 3 #include<cstring>
 4 #include<iostream>
 5 #include<cmath>
 6 #include<algorithm>
 7 using namespace std;
 8
 9 typedef long long LL;
10 const LL N=40000;
11 LL pl,bl;
12 LL p[N];
13 bool vis[N];
14 struct node{
15     LL d,id;
16 }bit[N];
17
18 bool cmp(node x,node y){
19     if(x.d==y.d) return x.id<y.id;
20     return x.d<y.d;
21 }
22
23 LL exgcd(LL a,LL b,LL &x,LL &y)
24 {
25     if(b==0) {x=1,y=0;return a;}
26     LL tx,ty;
27     LL d=exgcd(b,a%b,tx,ty);
28     x=ty;y=tx-(a/b)*ty;
29     return d;
30 }
31
32 LL find(LL x)
33 {
34     int l=1,r=bl;
35     while(l<=r)
36     {
37         int mid=(l+r)>>1;
38         if(bit[mid].d==x) return bit[mid].id;
39         if(bit[mid].d<x) l=mid+1;
40         if(bit[mid].d>x) r=mid-1;
41     }
42     return -1;
43 }
44
45 void exBSGS(LL b,LL &xx,LL &yy)
46 {
47     LL t,m,g,x,y,pm,am;
48     while(b%2==0) {b/=2;xx++;}
49     t=2;
50     for(int i=1;i<=100;i++)
51     {
52         if(t%b==1) {yy=i;return ;}
53         t=t*2%b;
54     }
55     m=(LL)(ceil((double)sqrt((double)b)));
56     pm=1%b;bit[0].d=1%b;bit[0].id=0;
57     for(int i=1;i<=m;i++)
58     {
59         bit[i].d=bit[i-1].d*2%b;
60         bit[i].id=i;
61         pm=pm*2%b;
62     }
63     sort(bit+1,bit+1+m,cmp);
64     bl=1;
65     for(int i=2;i<=m;i++)
66     {
67         if(bit[i].d!=bit[bl].d) bit[++bl]=bit[i];
68     }
69     exgcd(pm,b,x,y);
70     am=x%b+b;
71     t=1%b;
72     for(int i=0;i<=m;i++)
73     {
74         x=find(t);
75         if(x!=-1) {yy=i*m+x;return ;}
76         t=t*am%b;
77     }
78     return ;
79 }
80
81 int main()
82 {
83     freopen("a.in","r",stdin);
84     freopen("b.out","w",stdout);
85     LL T=0,a,b;
86     char c;
87     while(scanf("%I64d%c%I64d",&a,&c,&b)!=EOF)
88     {
89         LL x,y;
90         LL g=exgcd(a,b,x,y);
91         a/=g,b/=g;
92         x=1,y=-1;
93         exBSGS(b,x,y);
94         printf("Case #%I64d: %I64d,%I64d \n",++T,x,y);
95     }
96     return 0;
97 }

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<cmath>
#include<algorithm>
using namespace std;typedef long long LL;
const LL Max=(LL)1e6;
const LL N=Max+100;
LL fl;
LL f[N];LL gcd(LL a,LL b)
{if(b==0) return a;return gcd(b,a%b);
}bool cmp(int x,int y){return x<y;}LL eular(LL x)
{LL ans=x;for(int i=2;i*i<=x;i++){if(x%i==0) ans/=i,ans=ans*(i-1);while(x%i==0) x/=i;}if(x>1) ans/=x,ans=ans*(x-1);return ans;
}LL quickpow(LL a,LL b,LL mod)
{LL ans=1%mod;while(b){if(b&1) ans=ans*a%mod;a=a*a%mod;b>>=1;}return ans;
}void solve(LL b,LL &xx,LL &yy)
{LL k=2,x=b,ans=x;while(b%2==0) xx++,b/=2;LL phi=eular(b);for(int i=1;i*i<=phi;i++){if(phi%i==0) f[++fl]=i,f[++fl]=phi/i;}sort(f+1,f+1+fl,cmp);for(int i=1;i<=fl;i++){if(quickpow(2,f[i],b)==1) {yy=f[i];return ;}}
}int main()
{freopen("a.in","r",stdin);freopen("a.out","w",stdout);LL T=0,a,b;char c;while(scanf("%I64d%c%I64d",&a,&c,&b)!=EOF){LL x=1,y=0;LL g=gcd(a,b);a/=g,b/=g;solve(b,x,y);printf("Case #%I64d: %I64d,%I64d \n",++T,x,y);}return 0;
}