For a positive integer, $n$, define $g(n)$ to be the maximum perfect square that divides $n$.
For example, $g(18)=9$, $g(19)=1$.

Also define $${\displaystyle S(N)=\sum _{n=1}^{N}g(n)}$$

For example, $S(10)=24$ and $S(100)=767$.

Find $S({10}^{14})$. Give your answer modulo $1000000007$.