One day, Touma Kazusa encountered a easy math problem. Given $n$ and $k$, she need to calculate the following sum modulo $1e9 + 7$.
$\sum_{i=1}^{n}\sum_{j=1}^{n}gcd(i,j)^klcm(i, j)[gcd(i,j)\in prime]\% (1e9 + 7)$
However, as a poor student, Kazusa obviously did not, so Touma Kazusa went to ask Kitahara Haruki. But Kitahara Haruki is too busy, in order to prove that he is a skilled man, so he threw this problem to you. Can you answer this easy math problem quickly?