题目通道\]([\[NOI2016\] 循环之美 - 洛谷](https://www.luogu.com.cn/problem/P1587 "[NOI2016] 循环之美 - 洛谷")) ```cpp #include #include #include #include #define fp(i,a,b) for(int i=a,I=b;i<=I;++i) #define file(s) freopen(s".in","r",stdin),freopen(s".out","w",stdout) using namespace std; const int N=7e5+5,E=2e6+5; typedef int arr[N];typedef long long ll; struct Am{int nx,x,w;}e1[E]; struct Ans{int nx,n,m,k;ll w;}e2[E]; int n,m,k,M,c1,c2,K[2000],f1[E],f2[E];arr is,pr,mu,Smu; int Sm(int x){ if(x<=M)return Smu[x]; int u=(x+2017)%E; for(int i=f1[u];i;i=e1[i].nx)if(e1[i].x==x)return e1[i].w; e1[++c1]=Am{f1[u],x,1};f1[u]=c1; int&w=e1[c1].w,i=2,j=sqrt(x); for(;i<=j;++i)w-=Sm(x/i); for(;i<=x;i=j+1)j=x/(x/i),w-=(j-i+1)*Sm(x/i); return w; } ll sol(int n,int m,int k){ if(!n||!m)return 0; int u=(2017ll*n+m+k)%E; for(int i=f2[u];i;i=e2[i].nx)if(e2[i].n==n&&e2[i].m==m&&e2[i].k==k)return e2[i].w; e2[++c2]=Ans{f2[u],n,m,k,0};f2[u]=c2;ll&w=e2[c2].w; if(k==1){ if(n>m)swap(n,m); int i=1,j=sqrt(n),s,t=0,x,y; for(;i<=j;++i,t=s)s=Sm(i),w+=1ll*(n/i)*(m/i)*(s-t); for(;i<=n;i=j+1,t=s)x=n/i,y=m/i,j=min(n/x,m/y),s=Sm(j),w+=1ll*x*y*(s-t); u=(2017ll*m+n+k)%E;e2[++c2]=Ans{f2[u],m,n,k,w};f2[u]=c2; }else for(int i=1;i<=K[0]&&K[i]<=k;++i) if(k%K[i]==0&&mu[K[i]]) w+=sol(m/K[i],n,K[i])*mu[K[i]]; return w; } int main(){ #ifndef ONLINE_JUDGE file("s"); #endif scanf("%d%d%d",&n,&m,&k); M=min(N-5,max(k,min(n,m)));Smu[1]=mu[1]=1; fp(i,2,M){ if(!is[i])pr[++pr[0]]=i,mu[i]=-1; for(int j=1,x;j<=pr[0]&&(x=i*pr[j])<=M;++j){ is[x]=1;if(i%pr[j])mu[x]=-mu[i];else break; }Smu[i]=Smu[i-1]+mu[i]; } fp(i,1,k)if(k%i==0)K[++K[0]]=i; printf("%lld",sol(n,m,k)); return 0; } ```