1 #include<cmath> 2 #include<queue> 3 #include<cstdio> 4 #include<vector> 5 #include<cstdlib> 6 #include<cstring> 7 #include<iostream> 8 #include<algorithm> 9 #define N 10000010 10 #define RG register 11 #define mo 100000009 12 #define inf 0x3f3f3f3f 13 #define Inf 99999999999999999LL 14 using namespace std; 15 typedef long long LL; 16 bool vis[N]; 17 int T,m,n,ans,loc,top,f[N],pre[N],sta[N]; 18 inline int Abs(RG const int &a){return a>0?a:-a;} 19 inline int Max(RG const int &a,RG const int &b){return a>b?a:b;} 20 inline int Min(RG const int &a,RG const int &b){return a>b?b:a;} 21 inline int gi(){ 22 RG int x=0;RG bool flag=0;RG char c=getchar(); 23 while((c<'0'||c>'9')&&c!='-') c=getchar(); 24 if(c=='-') c=getchar(),flag=1; 25 while(c>='0'&&c<='9') x=x*10+c-'0',c=getchar(); 26 return flag?-x:x; 27 } 28 inline void init(){ 29 f[1]=1; 30 for (RG int i=2;i<N;++i){ 31 if(!vis[i]){ 32 f[i]=1-i; 33 sta[++top]=i; 34 } 35 for (RG int j=1;j<=top&&i*sta[j]<N;++j){ 36 vis[i*sta[j]]=1; 37 if(i%sta[j]==0){ 38 f[i*sta[j]]=f[i]; 39 break; 40 } 41 f[i*sta[j]]=((LL)f[i]*(LL)f[sta[j]])%mo; 42 } 43 } 44 for (RG int i=1;i<N;++i) pre[i]=(pre[i-1]+f[i])%mo; 45 } 46 inline LL sum(RG LL now){ 47 if(now&1) return (now+(LL)((now-1)/2)*now)%mo; 48 return (now+(LL)(now-1)*(now/2))%mo; 49 } 50 inline void work(){ 51 n=gi();m=gi(); 52 if(m<n) swap(m,n); 53 /*for (RG int i=1;i<=n;++i) 54 ans=( ans+ ( ( ( (LL)i*sum(n/i) )%mo *(LL)sum(m/i) )%mo *f[i])%mo )%mo;*/ 55 for (RG int i=1;i<=n;i=loc+1){ 56 //cout<<i<<endl; 57 loc=Min(m/(m/i),n/(n/i)); 58 //cout<<loc<<endl; 59 RG LL a=(sum(loc)-sum(i-1))%mo; 60 //cout<<"cfdsji"<<endl; 61 RG LL b=sum(m/i); 62 //cout<<"dsji"<<endl; 63 RG LL c=sum(n/i); 64 //cout<<"ji"<<endl; 65 RG LL d=(pre[loc]-pre[i-1])%mo; 66 cout<<a<<' '<<b<<' '<<c<<' '<<d<<endl; 67 cout<<"congratulations!"<<endl; 68 ans=(ans+( ( ((a*b)%mo) *c%mo) *d%mo))%mo; 69 } 70 printf("%d ",ans); 71 } 72 int main(){ 73 freopen("2394.in","r",stdin); 74 freopen("2394.out","w",stdout); 75 init(); 76 /*for (RG int i=1;i<=1000;++i) cout<<pre[i]<<' '; 77 cout<<endl;*/ 78 T=gi(); 79 while(T--) work(); 80 fclose(stdin); 81 fclose(stdout); 82 return 0; 83 }