HDU5514 Frogs

 /*
  HDU5514 Frogs
  http://acm.hdu.edu.cn/showproblem.php?pid=5514
  容斥原理
  *
  *
  */
 #include <cstdio>
 #include <cmath>
 #include <algorithm>
 //#define test
 using namespace std;
 const long long Nmax=1e5;
 long long n,m,a[Nmax];
 long long book[Nmax];
 long long p[Nmax];
 int cnt;
 long long num[Nmax];
 long long gcd(long long a,long long b)
 {
     if(b==0LL)
         return a;
     return gcd(b,a%b);
 }
 
 int main()
 {
     long long t;
     #ifdef test
     while()
     {
         long long a,b;
         scanf("%lld%lld",&a,&b);
         printf("%lld\n",gcd(a,b));
     }
     #endif
     scanf("%lld",&t);
     for(long long ttt=;ttt<=t;ttt++)
     {
         scanf("%lld%lld",&n,&m);
         int flag=;
         for(long long i=;i<=n;i++)
         {
             scanf("%lld",&a[i]);
             a[i]=gcd(a[i],m);
             if(a[i]==)
                 flag=;
         }
         if(flag)
         {
             long long ans=(m-1LL)*m/2LL;
             printf("Case #%lld: ",ttt);
             printf("%lld\n",ans);
             continue;
         }
         long long ans=0LL;
         cnt=;
         for(int i=;i*i<=m;i++)
         {
             if(m%i)
                 continue;
             p[++cnt]=i;
             if(i*i!=m)
                 p[++cnt]=m/i;
         }
         sort(p+,p++cnt);
         for(int i=;i<=cnt;i++)
             book[i]=num[i]=;
         for(int i=;i<=n;i++)
         {
             for(int j=;j<=cnt;j++)
                 if(p[j]%a[i]==)
                     book[j]=;
         }
         for(int i=;i<=cnt;i++)
         {
             if(book[i]!=num[i])
             {
                 long long tmp=m/p[i];
                 ans+=tmp*(tmp-1LL)/2LL*p[i]*(book[i]-num[i]);
                 tmp=book[i]-num[i];
                 for(int j=i+;j<=cnt;j++)
                     if(p[j]%p[i]==)
                         num[j]+=tmp;
             }
         }
 
         printf("Case #%lld: ",ttt);
         printf("%lld\n",ans);
     }
     return ;
 }