洛阳杯[数论][线性筛]

 

---

分析

(https://blog.youkuaiyun.com/forever_dreams/article/details/83450135)

---

#include<bits/stdc++.h>
#define N 100005
using namespace std;
int n,m,a[N],isp[N],prim[N],tot;
int g[N],ans;
bitset<1000000000> S;
int read(){
	int cnt=0; char ch=0;
	while(!isdigit(ch)) ch=getchar();
	while(isdigit(ch))cnt=cnt*10+(ch-'0'),ch=getchar();
	return cnt;
}
int gcd(int a,int b){return !b?a:gcd(b,a%b);}
void init(){
	for(int i=2;i<=N-5;i++){
		if(!isp[i]) isp[i]=1,prim[++tot]=i;
		for(int j=1;j<=tot && prim[j]*i<=N-5;j++){
			isp[i*prim[j]]=1;
			if(i%prim[j]==0) break;
		}
	} 
}
int divide(int x){
	int ans=0;
	for(int i=1;i<=tot && prim[i]*prim[i]<=x;i++){
		while(x%prim[i]==0) ans+=S[prim[i]]?-1:1,x/=prim[i];
	}
	if(x>1) ans+=S[x]?-1:1;
	return ans;
}
int main(){
	n=read(),m=read();
	for(int i=1;i<=n;i++) a[i]=read();
	for(int i=1;i<=m;i++) S[read()]=1;
	init();
	for(int i=1;i<=n;i++) ans+=divide(a[i]);
	for(int i=1;i<=n;i++) g[i]=gcd(g[i-1],a[i]);
	int div=1;
	for(int i=n;i>=1;i--){
		g[i]/=div;
		int x=divide(g[i]);
		if(x<0) ans+=i*(-x),div*=x;
	}
	printf("%d\n",ans);
	return 0;
}