bzoj2693

#include
#include
#include
#include
#include
using namespace std;
typedef long long LL;
inline int read()
{
    int x=0;bool f=0;char c=getchar();
    for (;c<'0'||c>'9';c=getchar()) f=c=='-'?1:0;
    for (;c>='0'&&c<='9';c=getchar()) x=x*10+c-'0';
    return f?-x:x;
}
const int N=10000010,mod=100000009;
int A,B,n,pr[N],pc=0,g[N],ans=0;
bool np[N];
 
inline int F(int x)
{
    int da=A/x,db=B/x;
    da=(LL)da*(da+1)/2%mod;
    db=(LL)db*(db+1)/2%mod;
    return (LL)da*db%mod;
}
 
inline int add(int a,int b)
{
    a+=b;
    if (a>=mod) a-=mod;
    return a;
}
 
int main()
{
    g[1]=1;n=N-1;
    for (int i=2;i<=n;i++)
    {
        if (!np[i]) pr[++pc]=i,g[i]=1-i;
        for (int j=1,k=i<<1;j<=pc&&k<=n;k=i*pr[++j])
        {
            np[k]=1;
            if (i%pr[j]==0) {g[k]=g[i];break;}
            g[k]=g[i]*(1-pr[j]);
        }
    }
    for (int i=1;i<=n;i++) g[i]=(LL)g[i]*i%mod;
    for (int i=1;i<=n;i++) g[i]=(g[i]+g[i-1]+(mod<<1))%mod;
	for (int cas=read();cas--;)
	{
		A=read();B=read();n=min(A,B);ans=0;
		for (int i=1,pos;i<=n;i=pos+1)
		{
			pos=min(A/(A/i),B/(B/i));
			ans=add(ans,(LL)(g[pos]-g[i-1]+mod)*F(i)%mod);
		}
		printf("%d\n",ans);
	}
    return 0;
}