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(1)
    {
        long long a,b;
        scanf("%lld%lld",&a,&b);
        printf("%lld
",gcd(a,b));
    }
    #endif
    scanf("%lld",&t);
    for(long long ttt=1;ttt<=t;ttt++)
    {
        scanf("%lld%lld",&n,&m);
        int flag=0;
        for(long long i=1;i<=n;i++)
        {
            scanf("%lld",&a[i]);
            a[i]=gcd(a[i],m);
            if(a[i]==1)
                flag=1;
        }
        if(flag)
        {
            long long ans=(m-1LL)*m/2LL;
            printf("Case #%lld: ",ttt);
            printf("%lld
",ans);
            continue;
        }
        long long ans=0LL;
        cnt=0;
        for(int i=2;i*i<=m;i++)
        {
            if(m%i)
                continue;
            p[++cnt]=i;
            if(i*i!=m)
                p[++cnt]=m/i;
        }
        sort(p+1,p+1+cnt);
        for(int i=1;i<=cnt;i++)
            book[i]=num[i]=0;
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=cnt;j++)
                if(p[j]%a[i]==0)
                    book[j]=1;
        }
        for(int i=1;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+1;j<=cnt;j++)
                    if(p[j]%p[i]==0)
                        num[j]+=tmp;
            }
        }

        printf("Case #%lld: ",ttt);
        printf("%lld
",ans);
    }
    return 0;
}