BZOJ 2693 jzptab（莫比乌斯反演）

#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
#define maxn 11111111
#define mod 100000009
typedef long long ll;
bool check[maxn];
int prime[maxn];
ll f[maxn],sum[maxn];
void Moblus(int n)
{
memset(check,0,sizeof(check));
f[1]=sum[1]=1;
int tot=0;
for(int i=2;i<=n;i++)
{
if(!check[i])
{
prime[tot++]=i;
f[i]=(i-1ll*i*i)%mod;
}
for(int j=0;j<tot;j++)
{
if(i*prime[j]>n)break;
check[i*prime[j]]=1;
if(i%prime[j]==0)
{
f[i*prime[j]]=(prime[j]*f[i])%mod;
break;
}
f[i*prime[j]]=(f[prime[j]]*f[i])%mod;
}
sum[i]=(sum[i-1]+f[i])%mod;
}
}
ll Sum(int x,int y)
{
return (1ll*x*(x+1)/2%mod)*(1ll*y*(y+1)/2%mod)%mod;
}
ll solve(int x,int y)
{
if(x>y)swap(x,y);
ll ans=0;
for(int i=1,next=0;i<=x;i=next+1)
{
next=min(x/(x/i),y/(y/i));
ans=(ans+(sum[next]-sum[i-1])*Sum(x/i,y/i)%mod+mod)%mod;
}
return ans;
}
int main()
{
Moblus(maxn-10);
int T,n,m;
scanf("%d",&T);
while(T--)
{
scanf("%d%d",&n,&m);
printf("%lld\n",solve(n,m));
}
return 0;
}