bzoj 2693 jzptab 莫比乌斯反演

题解

code:

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<ctime>
#include<cmath>
#include<algorithm>
#include<queue>
#include<set>
#include<map>
#include<iomanip>
using namespace std;
#define LL long long
#define up(i,j,n) for(LL i=j;i<=n;i++)
#define pii pair<LL,LL>
#define db double
#define eps 1e-4
#define FILE "dealing"
LL read(){
	LL x=0,f=1,ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch<='9'&&ch>='0'){x=(x<<1)+(x<<3)+ch-'0',ch=getchar();}
	return x*f;
}
const LL maxn=(LL)(1e7+3),inf=1000000000000000LL,limit=(LL)(1e7+2),mod=100000009;
bool cmin(LL& a,LL b){return a>b?a=b,true:false;}
bool cmax(LL& a,LL b){return a<b?a=b,true:false;}
LL n,m;
LL mu[maxn],b[maxn],H[maxn],prime[2000000],tail=0;
LL sum(LL x,LL y){
	x%=mod,y%=mod;
	return ((((x+1)*x)>>1)%mod)*((((y+1)*y)>>1)%mod)%mod;
}
void getmu(){
	mu[1]=1;H[1]=1;
	up(i,2,limit){
		if(!b[i])prime[++tail]=i,H[i]=(i-i*i)%mod;
		for(LL j=1;prime[j]*i<=limit;j++){
			b[i*prime[j]]=1;
			if(i%prime[j]){
				H[i*prime[j]]=(H[i]*H[prime[j]])%mod;
			}
			else {
				H[i*prime[j]]=H[i]*prime[j];
				break;
			}
		}
	}
	up(i,1,limit)H[i]=(H[i]+H[i-1])%mod;
}
int main(){
	freopen(FILE".in","r",stdin);
	freopen(FILE".out","w",stdout);
	LL q=read();
	getmu();
	while(q--){
		n=read(),m=read();
		if(n>m)swap(n,m);
		LL ans=0;
		up(i,1,n){
			LL pos=min(n/(n/i),m/(m/i));
			ans+=(H[pos]-H[i-1])*sum(n/i,m/i)%mod;
			ans%=mod;
			i=pos;
		}
		printf("%lld\n",(ans+mod)%mod);
	}
	return 0;
}