1 /*
2 HDU5514 Frogs
3 http://acm.hdu.edu.cn/showproblem.php?pid=5514
4 容斥原理
5 *
6 *
7 */
8 #include <cstdio>
9 #include <cmath>
10 #include <algorithm>
11 //#define test
12 using namespace std;
13 const long long Nmax=1e5;
14 long long n,m,a[Nmax];
15 long long book[Nmax];
16 long long p[Nmax];
17 int cnt;
18 long long num[Nmax];
19 long long gcd(long long a,long long b)
20 {
21 if(b==0LL)
22 return a;
23 return gcd(b,a%b);
24 }
25
26 int main()
27 {
28 long long t;
29 #ifdef test
30 while(1)
31 {
32 long long a,b;
33 scanf("%lld%lld",&a,&b);
34 printf("%lld\n",gcd(a,b));
35 }
36 #endif
37 scanf("%lld",&t);
38 for(long long ttt=1;ttt<=t;ttt++)
39 {
40 scanf("%lld%lld",&n,&m);
41 int flag=0;
42 for(long long i=1;i<=n;i++)
43 {
44 scanf("%lld",&a[i]);
45 a[i]=gcd(a[i],m);
46 if(a[i]==1)
47 flag=1;
48 }
49 if(flag)
50 {
51 long long ans=(m-1LL)*m/2LL;
52 printf("Case #%lld: ",ttt);
53 printf("%lld\n",ans);
54 continue;
55 }
56 long long ans=0LL;
57 cnt=0;
58 for(int i=2;i*i<=m;i++)
59 {
60 if(m%i)
61 continue;
62 p[++cnt]=i;
63 if(i*i!=m)
64 p[++cnt]=m/i;
65 }
66 sort(p+1,p+1+cnt);
67 for(int i=1;i<=cnt;i++)
68 book[i]=num[i]=0;
69 for(int i=1;i<=n;i++)
70 {
71 for(int j=1;j<=cnt;j++)
72 if(p[j]%a[i]==0)
73 book[j]=1;
74 }
75 for(int i=1;i<=cnt;i++)
76 {
77 if(book[i]!=num[i])
78 {
79 long long tmp=m/p[i];
80 ans+=tmp*(tmp-1LL)/2LL*p[i]*(book[i]-num[i]);
81 tmp=book[i]-num[i];
82 for(int j=i+1;j<=cnt;j++)
83 if(p[j]%p[i]==0)
84 num[j]+=tmp;
85 }
86 }
87
88 printf("Case #%lld: ",ttt);
89 printf("%lld\n",ans);
90 }
91 return 0;
92 }
