[杜教筛] BZOJ3512. DZY Loves Math IV

%%%Vectorxj
http://blog.csdn.net/vectorxj/article/details/78857079

#include 
#include 
#include 
#include 

using namespace std;

typedef pair<int,int> par;

const int N=1e6+10,P=1e9+7;

int mu[N],p[N],phi[N],fac[N],pre[N];

inline void Pre(const int &n){
  phi[1]=1; mu[1]=1; fac[1]=1;
  for(int i=2;i<=n;i++){
    if(!p[i])
      p[++*p]=i,phi[i]=i-1,mu[i]=-1,fac[i]=i;
    for(int j=1;j<=*p && 1LL*i*p[j]<=n;j++){
      p[i*p[j]]=1;
      if(i%p[j]){
    fac[i*p[j]]=fac[i]*p[j];
    phi[i*p[j]]=phi[i]*phi[p[j]];
    mu[i*p[j]]=-mu[i];
      }
      else{
    fac[i*p[j]]=fac[i];
    phi[i*p[j]]=phi[i]*p[j];
    break;
      }
    }
  }
  for(int i=1;i<=n;i++) pre[i]=(phi[i]+pre[i-1])%P;
}

mapint> M;
map<int,int> S;

int Phi(int n){
  if(n<=1000000) return pre[n];
  if(S.count(n)) return S[n];
  int ret=1LL*n*(n+1)/2%P;
  for(int i=2,j;i<=n;i=j+1){
    j=n/(n/i);
    ret=(ret-1LL*(j-i+1)*Phi(n/i))%P;
  }
  return S[n]=ret;
}

int Sum(int n,int m){
  if(!n || !m) return 0;
  if(M.count(par(n,m))) return M[par(n,m)];
  if(n==1) return Phi(m);
  if(m==1) return phi[n];
  if(!mu[n])
    return 1LL*n/fac[n]*Sum(fac[n],m)%P;
  int ret=0;
  for(int i=1;1LL*i*i<=n;i++){
    if(n%i) continue;
    ret=(ret+1LL*phi[n/i]*Sum(i,m/i))%P;
    if(i*i!=n)
      ret=(ret+1LL*phi[i]*Sum(n/i,m/(n/i)))%P;
  }
  return M[par(n,m)]=ret;
}

int main(){
  freopen("1.in","r",stdin);
  freopen("1.out","w",stdout);
  int n,m,ans=0; scanf("%d%d",&n,&m); Pre(1000000);
  for(int i=1;i<=n;i++)
    ans=(ans+Sum(i,m))%P;
  printf("%d\n",(ans+P)%P);
  return 0;
}