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dirichlet.hpp
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dirichlet.hpp
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#pragma once
template<typename T,bool multi,unsigned L=1010101010>struct Dirichlet{
ll N,P,Q;
vector<T> a,rui,A;
vector<ll> ps;
bool done=0;
Dirichlet(ll n):N(n),P(min<ll>(L,cbrt(n)*cbrt(n))),Q((n+P-1)/P),
a(P+1),rui(P+1),A(Q+1),done(0){}
const Dirichlet ident(){
Dirichlet res(N);
res.a.assign(P+1,0);
res.a[1]=1;
res.rui.assign(P+1,1);
res.A.assign(Q+1,1);
res.done=1;
return res;
}
void sieve(){
if(!ps.empty())return;
static bitset<L> isp;
rep(p,2,P+1)isp[p]=1;
for(ll p=2;p*p<=P;p++)if(isp[p]){
for(ll q=p*p;q<=P;q+=p)isp[q]=0;
}
rep(p,2,P+1)if(isp[p])ps.push_back(p);
}
void reset(){
a.assign(P+1,0);
rui.assign(P+1,0);
A.assign(Q+1,0);
done=0;
}
void ruith(){
rui.assign(P+1,0);
rep(i,1,P+1)rui[i]=rui[i-1]+a[i];
done=1;
}
Dirichlet operator*(const Dirichlet& x){
assert(done and x.done);
Dirichlet res(N);
if(multi){
sieve();
res.a=a;
for(auto& p:ps){
for(ll i=P/p;i>0;i--){
ll n=p*i,q=p,m=i;
for(;;){
res.a[n]+=x.a[q]*res.a[m];
if(m%p)break;
q*=p,m/=p;
}
}
}
}
else{
rep(i,1,P+1)rep(j,1,P/i+1){
res.a[i*j]+=a[i]*x.a[j];
}
}
res.ruith();
rep(i,1,Q+1){
ll n=N/i,M=int(sqrt(n));
rep(j,1,M+1){
if(n/j<=P)res.A[i]+=a[j]*x.rui[n/j]+x.a[j]*rui[n/j];
else res.A[i]+=a[j]*x.A[i*j]+x.a[j]*A[i*j];
if(M<=P)res.A[i]-=x.a[j]*rui[M];
else res.A[i]-=x.a[j]*A[N/M];
}
}
return res;
}
Dirichlet operator/(const Dirichlet& x){
assert(done and x.done);
Dirichlet res=*this;
if(multi){
sieve();
for(auto& p:ps){
rep(i,1,P/p+1){
int n=p*i,q=p,m=i;
for(;;){
res.a[n]-=x.a[q]*res.a[m];
if(m%p)break;
q*=p,m/=p;
}
}
}
}
else{
rep(i,1,P)rep(j,2,P/i+1){
res.a[i*j]-=res.a[i]*x.a[j];
}
}
res.ruith();
for(int i=Q;i>0;i--){
ll n=N/i,M=int(sqrt(n));
rep(j,1,M+1){
if(n/j<=P){
if(j!=1)res.A[i]-=x.a[j]*res.rui[n/j];
res.A[i]-=res.a[j]*x.rui[n/j];
}
else{
if(j!=1)res.A[i]-=x.a[j]*res.A[i*j];
res.A[i]-=res.a[j]*x.A[i*j];
}
if(M<=P)res.A[i]+=res.a[j]*x.rui[M];
else res.A[i]+=res.a[j]*x.A[N/M];
}
}
return res;
}
Dirichlet pow(ll t){
assert(done);
Dirichlet res=ident(),b=*this;
while(t){
if(t&1)res=res*b;
b=b*b;
t>>=1;
}
return res;
}
const T& operator[](ll x){
assert(done);
if(x<=P)return rui[x];
else return A[N/x];
}
};
/**
* @brief Dirichlet series
*/