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OI-codes/Luogu/P4449/P4449.cpp

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#include <bits/stdc++.h>
using namespace std;
const long long N = 6000010;
const long long mod = 1000000007;
long long n, m, k, t;
long long ans, powk[N], vis[N], f[N], pri[N], tot;
long long qpow(long long a, long long b) {
long long res = 1;
while (b) {
if (b & 1) res = res * a % mod;
a = a * a % mod;
b >>= 1;
}
return res;
}
void euler(long long n) {
f[1] = 1;
vis[1] = 1;
for (long long i = 2; i <= n; i++) {
if (!vis[i]) pri[++tot] = i, f[i] = (powk[i] - 1 + mod) % mod;
for (long long j = 1; j <= tot && i * pri[j] <= n; ++j) {
vis[i * pri[j]] = 1;
if (i % pri[j] == 0) {
f[i * pri[j]] = f[i] * powk[pri[j]] % mod;
break;
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} else {
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f[i * pri[j]] = f[i] * f[pri[j]] % mod;
}
}
}
}
int main() {
cin >> t >> k;
for (long long i = 1; i <= 5000000; i++) {
powk[i] = qpow(i, k);
}
euler(5000000);
for (long long i = 1; i <= 5000000; i++) {
f[i] = (f[i] + f[i - 1]) % mod;
}
while (t--) {
cin >> n >> m;
ans = 0;
for (long long l = 1, r; l <= min(n, m); l = r + 1) {
r = min(n / (n / l), m / (m / l));
ans += (n / l) * (m / l) % mod * ((f[r] - f[l - 1] + mod) % mod) % mod;
ans %= mod;
}
cout << ans << endl;
}
return 0;
}