A multiplicative function $f(x)$ is a function over positive integers satisfying $f(1)=1$ and $f(ab)=f(a)f(b)$ for any two coprime positive integers $a$ and $b$.

For integer $k$ let $f_k(n)$ be a multiplicative function additionally satisfying $f_k(p^e)=p^k$ for any prime $p$ and any integer $e>0$.
For example, $f_1(2)=2$, $f_1(4)=2$, $f_1(18)=6$ and $f_2(18)=36$.

Let ${\displaystyle S_k(n)=\sum _{i=1}^n{f}_k(i)}$. For example, $S_1(10)=41$, $S_1(100)=3512$, $S_2(100)=208090$, $S_1(10000)=35252550$ and ${\displaystyle \sum _{k=1}^3{S}_k({10}^8)\equiv 338787512(\mathrm{mod}1000000007)}$.

Find ${\displaystyle \sum _{k=1}^{50}{S}_k({10}^{12})mod1000000007}$.