1 #include<cmath>
 2 #include<cstdio>
 3 #include<cstdlib>
 4 #include<cstring>
 5 #include<iostream>
 6 #include<algorithm>
 7 using namespace std;
 8 typedef long long ll;
 9 const int maxn = 1e7 + 1;
10 const int mod = 1e8 + 9;
11 int cnt;
12 int h[maxn];
13 int pri[maxn];
14 int sum[maxn];
15 bool vis[maxn];
16 inline void Scan(int &x)
17 {
18     char c;
19     bool o = false;
20     while(!isdigit(c = getchar())) o = (c != ‘-‘) ? o : true;
21     x = c - ‘0‘;
22     while(isdigit(c = getchar())) x = x * 10 + c - ‘0‘;
23     if(o) x = -x;
24 }
25 inline void Sieve()
26 {
27     h[1] = 1;
28     for(int i = 2; i <= maxn; ++i)
29     {
30         if(!vis[i]) pri[++cnt] = i, h[i] = ((-(long long) i * i % mod) + mod + i) % mod;
31         for(int j = 1; j <= cnt; ++j)
32         {
33             int s = pri[j];
34             long long k = (long long) i * s;
35             if(k > maxn) break;
36             vis[k] = true;
37             if(!(i % s))
38             {
39                 h[k] = (long long) s * h[i] % mod;
40                 break;
41             }
42             else h[k] = (long long) h[s] * h[i] % mod;
43         }
44     }
45     for(int i = 1; i <= maxn; ++i) sum[i] = (sum[i - 1] + h[i]) % mod;
46 }
47 inline int Sum(int n, int m)
48 {
49     return ((long long) n * (n + 1) >> 1) % mod * (((long long) m * (m + 1) >> 1) % mod) % mod;
50 }
51 inline int Mobius(int n, int m)
52 {
53     int res = 0, last = 0;
54     if(n > m) swap(n, m);
55     for(int i = 1; i <= n; i = last + 1)
56     {
57         last = min(n / (n / i), m / (m / i));
58         res = (res + (long long) Sum(n / i, m / i) * ((sum[last] - sum[i - 1] + mod) % mod) % mod) % mod;
59     }
60     return res;
61 }
62 int main()
63 {
64     Sieve();
65     int n;
66     Scan(n);
67     int a, b;
68     while(n--)
69     {
70         Scan(a), Scan(b);
71         printf("%d\n", Mobius(a, b));
72     }
73 }