反演+容斥
#include <iostream>
#include <cstdio>
#define LL long long
using namespace std;
LL read()
{
LL x=0,f=1;
char c=getchar();
while(c<'0'||c>'9')
{
if(c=='-') f=-1;
c=getchar();
}
while(c>='0'&&c<='9')
{
x=x*10+c-'0';
c=getchar();
}
return f*x;
}
const int N=60000;
LL n,m,a,b,mu[N],sum[N],k,t,prime[N],next,ans,num;
bool f[N];
int main()
{
n=50000; mu[1]=1; f[1]=1;
for(int i=2;i<=n;i++)
{
if(!f[i])
{
prime[++num]=i;
mu[i]=-1;
}
for(int j=1;j<=num&&i*prime[j]<=n;j++)
{
f[i*prime[j]]=1;
mu[i*prime[j]]=-mu[i];
if(i%prime[j]==0)
{
mu[i*prime[j]]=0;
break;
}
}
}
for(int i=1;i<=n;i++) sum[i]=sum[i-1]+mu[i];
t=read();
while(t--)
{
a=read()-1; n=read(); b=read()-1; m=read(); k=read();
ans=0;
n/=k; m/=k;
for(int i=1;i<=min(n,m);i=next)
{
next=min(n/(n/i),m/(m/i))+1;
ans+=(sum[next-1]-sum[i-1])*(n/i)*(m/i);
}
a/=k; b/=k;
for(int i=1;i<=min(a,b);i=next)
{
next=min(a/(a/i),b/(b/i))+1;
ans+=(sum[next-1]-sum[i-1])*(a/i)*(b/i);
}
for(int i=1;i<=min(a,m);i=next)
{
next=min(a/(a/i),m/(m/i))+1;
ans-=(sum[next-1]-sum[i-1])*(a/i)*(m/i);
}
for(int i=1;i<=min(b,n);i=next)
{
next=min(b/(b/i),n/(n/i))+1;
ans-=(sum[next-1]-sum[i-1])*(b/i)*(n/i);
}
cout<<ans<<"\n";
}
return 0;
}