【BZOJ】【P2693】【jzptab】【题解】【莫比乌斯反演】

传送门:http://www.lydsy.com/JudgeOnline/problem.php?id=2693

题解见下一篇

Code:

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;
const int maxn=10000005;
typedef long long LL;
int MOD=100000009;
LL n,m;
bool p[maxn];
int prime[maxn],minp[maxn];
int u[maxn];
LL f[maxn];
int getint(){
	int res=0;char c=getchar();
	while(!isdigit(c))c=getchar();
	while(isdigit(c))res=res*10+c-'0',c=getchar();
	return res;
}
void init(int maxn){
	f[1]=1;
	for(int i=2;i<maxn;i++){
		if(!p[i]){
			prime[++prime[0]]=i;minp[i]=i;f[i]=(1-i)%MOD;
		}for(int j=1;j<=prime[0]&&i*prime[j]<maxn;j++){
			p[i*prime[j]]=1;
			if(i%prime[j]==0){
				minp[i*prime[j]]=minp[i]*prime[j];
				f[i*prime[j]]=(LL)(1-prime[j])*f[i*prime[j]/minp[i*prime[j]]]%MOD; 
				break;
			}else{
				minp[i*prime[j]]=prime[j];
				f[i*prime[j]]=(LL)f[i]*f[prime[j]]%MOD;
			}
		}
	}
	for(int i=1;i<maxn;i++)f[i]=(f[i]*i)%MOD;
	for(int i=2;i<maxn;i++)f[i]=(f[i-1]+f[i])%MOD;
}
int main(){
	init(maxn);
	int _=getint();
	while(_--){
		n=getint();m=getint();
		LL ans=0;
		if(n>m)swap(n,m);
		for(int i=1,last;i<=n;i=last+1){
			last=min(n/(n/i),m/(m/i));
			LL tmp=(LL)((LL)n/i*(n/i+1)/2%MOD)%MOD*(LL)((LL)m/i*(m/i+1)/2%MOD)%MOD;
			ans=((LL)(f[last]-f[i-1])%MOD*tmp%MOD+ans)%MOD;
		}while(ans<0)ans+=MOD;
		printf("%d\n",ans%MOD);
	}
	return 0;
}