1 //Author: xiaowuga
 2 #include <bits/stdc++.h>
 3 using namespace std;
 4 #define inf 0x3f3f3f3f
 5 #define MAX INT_MAX
 6 #define mem(s,ch) memset(s,ch,sizeof(s))
 7 const long long N=100000;
 8 const long long mod=1e9+7;
 9 typedef long long LL;
10 typedef int II;
11 typedef unsigned long long ull;
12 #define nc cout<<"nc"<<endl
13 #define endl "\n"
14 vector<LL>Euler;
15 void init_Euler(II n){
16     Euler.resize(n+1);
17     Euler[0]=0;
18     Euler[1]=1;
19     for(LL i=2;i<n;i++) Euler[i]=i;
20     for(LL i=2;i<n;i++){
21         if(Euler[i]==i){
22             for(LL j=i;j<n;j+=i)
23                 Euler[j]=Euler[j]/i*(i-1);//先进行除法防止溢出
24         }
25     }
26     for(II i=1;i<n;i++){
27         Euler[i]+=Euler[i-1];
28     }
29 }
30 int solve(II n,II m){
31     vector<II>p;
32     for(II i=2;i*i<=m;i++){
33         if(m%i==0){
34             p.push_back(i);
35             while(m%i==0) m/=i;
36         }
37     }
38     if(m>1) p.push_back(m);
39     II sz=p.size();
40     LL sum=0;
41     for(II i=1;i<(1<<sz);i++){
42         II ct=0;
43         LL mul=1;
44         for(II j=0;j<sz;j++){
45             if(i&(1<<j)){
46                 ct++;
47                 mul*=p[j];
48             }
49         }
50         if(ct&1) sum+=n/mul;
51         else sum-=n/mul;
52     }
53     return n-sum;
54 }
55 int main() {
56     ios::sync_with_stdio(false);cin.tie(0);
57     II a,b,c,d,k;
58     II T,ca=0;
59     init_Euler(100000+1000);
60     cin>>T;
61     while(T--){
62         cin>>a>>b>>c>>d>>k;
63         if(k==0||k>b||k>d){
64             cout<<"Case "<<++ca<<": "<<0<<endl;
65             continue;
66         }
67         if(b>d) swap(b,d);
68         b/=k;d/=k;
69         LL ans=Euler[b];
70         for(II i=b+1;i<=d;i++){
71             ans+=solve(b,i);
72         }
73         cout<<"Case "<<++ca<<": "<<ans<<endl;
74     }
75     return 0;
76 }

 1 //Author: xiaowuga
 2 #include<iostream>
 3 #include<vector>
 4 using namespace std;
 5 #define inf 0x3f3f3f3f
 6 #define MAX INT_MAX
 7 #define mem(s,ch) memset(s,ch,sizeof(s))
 8 const long long N=100000;
 9 const long long mod=1e9+7;
10 typedef long long LL;
11 typedef int II;
12 typedef unsigned long long ull;
13 #define nc cout<<"nc"<<endl
14 #define endl "\n"
15 LL solve(II r,LL n){
16     vector<int>p;
17     for(II i=2;i*i<=r;i++){
18         if(r%i==0){
19             p.push_back(i);
20             while(r%i==0) r/=i;
21         }
22     }
23     if(r>1) p.push_back(r);
24     LL sum=0;
25     for(LL i=1;i<(1<<p.size());i++){
26         LL d=1,ct=0;
27         for(II j=0;j<p.size();j++){
28             if(i&(1<<j)){
29                 ct++;
30                 d*=p[j];
31             }
32         }
33         if(ct%2) sum+=n/d;
34         else sum-=n/d;
35     }
36     return n-sum;
37 }
38 int main() {
39     ios::sync_with_stdio(false);cin.tie(0);
40     II n,k;
41     while(cin>>n>>k){
42         LL l=1,r=inf*2;
43         LL ans=1;
44         while(l<r){
45             LL m=l+(r-l)/2;
46             LL t=solve(n,m);
47             if(t>=k){
48                if(t==k) ans=m;
49                r=m;
50             }
51             else{
52                 l=m+1;
53             }
54         }
55         cout<<ans<<endl;
56     }
57     return 0;
58 }