HDU5780 gcd (BestCoder Round #85 E) 欧拉函数预处理——分块优化

#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <algorithm>
using namespace std;
typedef  long long LL;
const int N = 1e6+5;
const LL mod = 1e9+7;
int phi[N],T;
LL sum[N],x,n;
LL qpow(LL a,LL b){
  LL ret=1;
  while(b){
    if(b&1)ret=(ret*a)%mod;
    b>>=1;
    a=(a*a)%mod;
  }
  return ret;
}
inline void up(LL &x,LL y){
  x+=y;if(x>=mod)x-=mod;
}
int main(){
  phi[1]=1;
  for(int i=2;i<=N-5;++i)if(!phi[i]){
    for(int j=i;j<=N-5;j+=i){
      if(!phi[j])phi[j]=j;
        phi[j]=phi[j]/i*(i-1);
    }
  }
  for(int i=1;i<=N-5;++i)sum[i]=sum[i-1]+1ll*phi[i];
  scanf("%d",&T);
  while(T--){
    scanf("%I64d%I64d",&x,&n);
    if(x==1){
      printf("0\n");continue;
    }
    LL inv=qpow(x-1,mod-2),ret=0;
    for(int i=1,j;i<=n;i=j+1){
      j=n/(n/i);
      LL a0=qpow(x,i),qn=qpow(x,j-i+1);
      up(qn,mod-1);
      a0=a0*qn%mod*inv%mod;
      up(a0,mod-(j-i+1));
      a0=(2ll*sum[n/i]-1)%mod*a0%mod;
      up(ret,a0);
    }
    printf("%I64d\n",ret);
  }
  return 0;
}