For any integer $n>0$ and prime number $p,$ define ${\nu }_p(n)$ as the greatest integer $r$ such that $p^r$ divides $n$.

Define $$D(n,m)=\sum _{p\text{ prime}}|{\nu }_p(n)-{\nu }_p(m)|.$$ For example, $D(14,24)=4$.

Furthermore, define $$S(N)=\sum _{1\le n,m\le N}D(n,m).$$ You are given $S(10)=210$ and $S({10}^2)=37018$.

Find $S({10}^{12})$. Give your answer modulo $1000000007$.