[Training school] Xiaoqiu count

The meaning of problems

Xiaoqiu want to know how many arrays \ (a_1, a_2, ..., a_k \) satisfies \ (gcd (a_1, a_2, ..., a_k) = d \) and \ (lcm (a_1, a_2, a_k ...) = n-\) , two arrays as different, as long as the presence of a number of different positions of the two

Thinking

Although this question is not the original title

The \ (d, n \) prime factorisation, for each quality factor, a factor of at least a minimum number of, at least a factor of the maximum number, can be used repellent capacity, i.e. Collection - a + 2 does not satisfy Satisfy

Code

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll mod = 1000000007;
int k,d,n;

ll quickpow(ll a,ll b)
{
    ll ret=1;
    while(b)
    {
        if(b&1) ret=ret*a%mod;
        a=a*a%mod;
        b>>=1;
    }
    return ret;
}
int main()
{
    cin>>k>>d>>n;
    ll ans=1;
    for(int i=2;i*i<=n;++i)
    {
        if(n%i==0)
        {
            int cnt1=0,cnt2=0;
            while(n%i==0) ++cnt1,n/=i;
            while(d%i==0) ++cnt2,d/=i;
            if(cnt1==cnt2) continue;//注意判相等
            ans = ans * ((quickpow(cnt1-cnt2+1,k) - 2ll * quickpow(cnt1-cnt2,k) + quickpow(cnt1-cnt2-1,k))%mod) %mod;
        }
    }
    if(d==1 && n>1) ans = ans * (quickpow(2,k)-2) %mod;
    cout<<(ans%mod+mod)%mod<<endl;
    return 0;
}