1 #include<bits/stdc++.h> 2 #define ll long long 3 #define R register 4 using namespace std; 5 const int N=10000010,mod=100000009; 6 int n,m,p[N],tot; 7 ll f[N]; 8 bool isp[N]; 9 int read(){ 10 int x=0;char c=0; 11 while(c<'0'||c>'9') c=getchar(); 12 while(c>='0'&&c<='9') x=(x<<3)+(x<<1)+c-48,c=getchar(); 13 return x; 14 } 15 void getf(int lim){ 16 f[1]=1; 17 for(R int i=2;i<=lim;i++){ 18 if(!isp[i]) p[++tot]=i,f[i]=(1LL*(1-i)*i%mod+mod)%mod; 19 for(R int j=1;j<=tot&&1LL*p[j]*i<=lim;j++){ 20 isp[i*p[j]]=1; 21 if(i%p[j]){f[i*p[j]]=f[i]*f[p[j]]%mod;} 22 else{ 23 f[i*p[j]]=f[i]*p[j]%mod; 24 break; 25 } 26 } 27 } 28 for(int i=2;i<=lim;i++) f[i]=(f[i]+f[i-1])%mod; 29 return; 30 } 31 void solve(){ 32 n=read(),m=read(); 33 if(n>m) swap(n,m); 34 R int l=1,r; 35 ll ans=0; 36 while(l<=n){ 37 r=min(n/(n/l),m/(m/l)); 38 ll temp=(1LL*(n/l+1)*(n/l)/2%mod)*(1LL*(m/l+1)*(m/l)/2%mod)%mod; 39 ans=((ans+temp*(f[r]-f[l-1]))%mod+mod)%mod; 40 l=r+1; 41 } 42 printf("%lld ",ans); 43 return; 44 } 45 int main(){ 46 getf(10000000); 47 int T; 48 T=read(); 49 while(T--) solve(); 50 return 0; 51 }