Enhanced perfect power

A perfect power $n$ is called enhanced if there exists two integers $m>0$ and $k>2$ such that $n=m^k$. The enhanced perfect powers no more than $100$ are $1,8,16,27,32,64,81$.

Let $S(N)$ be the sum of all enhanced perfect powers no more than $N$. You are given $S(100)=229$, $S(10000)=99352$ and $S({10}^8)\mathrm{mod}1000000007=553225565$.

Find $S({10}^{100})\mathrm{mod}1000000007$.