1 #include<bits/stdc++.h>
2 using namespace std;
3 #define ll long long
4 #define mod 100000009
5 #define N 10000005
6 ll t,n,m,ans,c[N],f[N],vis[N],p[N];
7 int main(){
8 scanf("%lld",&t);
9 f[1]=c[1]=1;
10 for(int i=2;i<=N-5;i++){
11 c[i]=1LL*i*(i+1)/2%mod;
12 if (!vis[i])f[p[++p[0]]=i]=(1LL-i)*i%mod+mod;
13 for(int j=1;j<=p[0];j++){
14 if (i*p[j]>N-5)break;
15 vis[i*p[j]]=1;
16 if (i%p[j])f[i*p[j]]=f[i]*f[p[j]]%mod;
17 else{
18 f[i*p[j]]=f[i]*p[j]%mod;
19 break;
20 }
21 }
22 }
23 for(int i=2;i<=N-5;i++)f[i]=(f[i]+f[i-1])%mod;
24 while (t--){
25 scanf("%lld%lld",&n,&m);
26 ans=0;
27 if (n>m)swap(n,m);
28 for(int i=1,j;i<=n;i=j+1){
29 j=min(n/(n/i),m/(m/i));
30 ans=(ans+c[n/i]*c[m/i]%mod*(f[j]-f[i-1]+mod))%mod;
31 }
32 printf("%lld\n",ans);
33 }
34 }
