[bzoj2693]jzptab

#include<bits/stdc++.h> 
using namespace std;
#define ll long long
#define mod 100000009
#define N 10000005
ll t,n,m,ans,c[N],f[N],vis[N],p[N];
int main(){
    scanf("%lld",&t);
    f[1]=c[1]=1;
    for(int i=2;i<=N-5;i++){
        c[i]=1LL*i*(i+1)/2%mod;
        if (!vis[i])f[p[++p[0]]=i]=(1LL-i)*i%mod+mod;
        for(int j=1;j<=p[0];j++){
            if (i*p[j]>N-5)break;
            vis[i*p[j]]=1;
            if (i%p[j])f[i*p[j]]=f[i]*f[p[j]]%mod;
            else{
                f[i*p[j]]=f[i]*p[j]%mod;
                break;
            }
        }
    }
    for(int i=2;i<=N-5;i++)f[i]=(f[i]+f[i-1])%mod;
    while (t--){
        scanf("%lld%lld",&n,&m);
        ans=0;
        if (n>m)swap(n,m);
        for(int i=1,j;i<=n;i=j+1){
            j=min(n/(n/i),m/(m/i));
            ans=(ans+c[n/i]*c[m/i]%mod*(f[j]-f[i-1]+mod))%mod;
        }
        printf("%lld\n",ans);
    }
}