传送门
![Ans=\sum_{a_1=l}^r\sum_{a_2=l}^r...\sum_{a_n=l}^r[gcd(a_1,a_2,...,a_n)=k] P3172 [CQOI2015]选数 [莫比乌斯反演+杜教筛]_整除](https://file.cfanz.cn/uploads/gif/2022/07/12/7/T1T6LZ7e91.gif)
![=\sum_{a_1=l/k}^{r/k}\sum_{a_2=l/k}^{r/k}...\sum_{a_n=l/k}^{r/k}[gcd(a_1,a_2,...,a_n)=1] P3172 [CQOI2015]选数 [莫比乌斯反演+杜教筛]_#define_02](https://file.cfanz.cn/uploads/gif/2022/07/12/7/T1b6I006bX.gif)
![=\sum_{d=1}^{r/k}\mu(d)(r/kd-(l-1)/kd)^n P3172 [CQOI2015]选数 [莫比乌斯反演+杜教筛]_i++_03](https://file.cfanz.cn/uploads/gif/2022/07/12/7/A23ce6RR12.gif)
然后就是整除分块+杜教筛
#include<bits/stdc++.h>
#define N 5000050
#define Mod 1000000007
#define LL long long
using namespace std;
int n,k,L,R;
int prim[N], isp[N], tot, mu[N];
map<int,int> Mu;
LL power(LL a,int b){
LL ans = 1;
for(;b;b>>=1){
if(b&1) ans = (ans*a) % Mod;
a = (a*a) % Mod;
} return ans;
}
void prework(){
mu[1] = 1;
for(int i=2;i<=N-50;i++){
if(!isp[i]) prim[++tot] = i, mu[i] = -1;
for(int j=1;j<=tot;j++){
if(prim[j] * i > N - 50) break;
isp[prim[j] * i] = 1;
if(i % prim[j] == 0) break;
mu[prim[j] * i] = -mu[i];
}
}
for(int i=2;i<=N-50;i++) mu[i] += mu[i-1];
}
int getf(int x){
if(x<=N-50) return mu[x];
if(Mu[x]) return Mu[x];
int ans = 1;
for(int l=2,r;l<=x;l=r+1){
int val = x/l; r = x/val;
ans -= (r-l+1) * getf(val) % Mod;
ans = (ans % Mod + Mod) % Mod;
} return Mu[x] = ans;
}
int main(){
prework();
scanf("%d%d%d%d",&n,&k,&L,&R);
L--; L/=k, R/=k;
LL ans = 0;
for(int l=1,r; l<=R; l=r+1){
int v1 = L/l, v2 = R/l;
if(v1 == 0) r = R/v2;
else r = min(L/v1, R/v2);
ans += (LL)(getf(r) - getf(l-1)) * power(v2-v1, n) % Mod;
ans = (ans % Mod + Mod) % Mod;
} printf("%lld",ans); return 0;
}









