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lightoj 1054.cpp
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lightoj 1054.cpp
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#include<bits/stdc++.h>
using namespace std;
#define mx 100005
#define ll long long
#define mod 1000000007
int ar[mx];
char ch[mx];
vector<int>prime;
bool f[mx];
int n,m,k,ii;
ll bigmod(ll e,ll x)
{
if(!x)return 1;
ll p=bigmod(e,x/2);
p=(p*p)%mod;
if(x%2)p=(p*e)%mod;
return p;
}
void seive()
{
for(int i=2;i<=100005;i++)
{
if(f[i]==false)
{
prime.push_back(i);
for(ll j=1LL*i*i;j<=(ll)100005;j+=i)
{
f[j]=true;
}
}
}
}
void solve()
{
scanf("%d%d",&n,&m);
if(n==mod)
{
printf("Case %d: 1\n",++ii);
return;
}
vector<pair<int,int>>tem;
int sz=prime.size();
for(int i=0;i<sz && (ll)prime[i]*prime[i]<=(ll)n;i++)
{
if(n%prime[i]==0)
{
int cnt=0;
while(n%prime[i]==0)
{
n/=prime[i];
cnt++;
}
tem.push_back({prime[i],cnt});
}
}
if(n>1)tem.push_back({n,1});
ll re=1;
for(auto it:tem)
{
// cout<<it.first<<" "<<it.second<<endl;
ll p=it.first;
ll e=(ll)it.second*m+1;
// cout<<p<<" "<<e<<endl;
ll x=(bigmod(p,e)-1+mod)%mod;
ll y=bigmod(p-1,mod-2);
x=(x*y)%mod;
// cout<<x<<endl;
re=(re*x)%mod;
// cout<<re<<endl;
}
printf("Case %d: %lld\n",++ii,re);
}
/*
1
22 4
*/
int main()
{
//freopen("in.txt","r",stdin);
//freopen("out.txt","w",stdout);
int t=1;
seive();
scanf("%d",&t);
while(t--)solve();
return 0;
}