【BZOJ】【P2154】【Crash的数字表格】【题解】【莫比乌斯反演】

传送门:http://www.lydsy.com/JudgeOnline/problem.php?id=2154

题解:http://www.cnblogs.com/jianglangcaijin/archive/2013/11/27/3446169.html

Rank里时间分成了200ms-900ms和3000ms+两大波

似乎有更优做法?有待研究

Code:

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;
const int maxn=1e7+5;
typedef long long LL;
int MOD=20101009;
int n,m;
bool p[maxn];
int prime[maxn];
LL u[maxn];
void init(int maxn){
u[1]=1;
for(int i=2;i<maxn;i++){
if(!p[i]){
prime[++prime[0]]=i;u[i]=-1;
}for(int j=1;j<=prime[0]&&i*prime[j]<maxn;j++){
p[i*prime[j]]=1;
if(i%prime[j]==0){
u[i*prime[j]]=0;break;
}else u[i*prime[j]]=-u[i];
}
}for(int i=2;i<maxn;i++)u[i]=(u[i-1]+(LL)(i*u[i]%MOD*i))%MOD;
}
inline LL S(LL n,LL m){
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 Sum=(n/i*(n/i+1)/2%MOD)*(m/i*(m/i+1)/2%MOD)%MOD;
ans=(ans+(LL)(u[last]-u[i-1])*Sum%MOD)%MOD;
}return ans;
}
int main(){
cin>>n>>m;
LL ans=0;
if(n>m)swap(n,m);
init(m+1);
for(int i=1,last;i<=n;i=last+1){
last=min(n/(n/i),m/(m/i));
ans=(ans+(LL)(i+last)*(last-i+1)/2*(S(n/i,m/i)))%MOD;
}while(ans<0)ans+=MOD;
cout<<ans%MOD<<endl;
return 0;
}