GCD

传送门：

#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
using namespace std;
#define ll long long
#define re register
const int N=1e5+10;
const int M=1e5;
void read(int &a)
{
    a=0;
    int d=1;
    char ch;
    while(ch=getchar(),!isdigit(ch))
        if(ch=='-')
            d=-1;
    a=ch^48;
    while(ch=getchar(),isdigit(ch))
        a=(a<<3)+(a<<1)+(ch^48);
    a*=d;
}
void write(int x)
{
    if(x<0)
        putchar(45),x=-x;
    if(x>9)
        write(x/10);
    putchar(x%10+'0');
}
int pri[N],cnt;
ll mu[N];
bool vis[N];
inline void init()
{
    mu[1]=1;
    for(re int i=2;i<=M;i++)
    {
        if(!vis[i])
            pri[++cnt]=i,mu[i]=-1;
        for(re int j=1;j<=cnt&&i*pri[j]<=M;j++)
        {
            vis[i*pri[j]]=1;
            if(i%pri[j]==0)
                break;
            mu[i*pri[j]]=-mu[i];
        }
    }
    for(re int i=1;i<=M;i++)
        mu[i]+=mu[i-1];
}
int main()
{
    init();
    int T,cas=0;
    read(T);
    while(T--)
    {
        cas++;
        int a,b,c,d,k;
        read(a);
        read(b);
        read(c);
        read(d);
        read(k);
        if(k==0)
        {
            printf("Case %d: 0
",cas);
            continue;
        }
        b/=k;
        d/=k;
        if(b>d)
            swap(b,d);
        ll ans1=0,ans2=0;
        for(re int l=1,r;l<=b;l=r+1)
        {
            r=min(b/(b/l),d/(d/l));
            ans1+=(mu[r]-mu[l-1])*(b/l)*(d/l);
        }
        for(re int l=1,r;l<=b;l=r+1)
        {
            r=b/(b/l);
            ans2+=(mu[r]-mu[l-1])*(b/l)*(b/l);
        }
        ll ans=ans1-ans2/2;
        printf("Case %d: %lld
",cas,ans);
    }
    return 0;
}