Let $n$ be a positive integer and let $E_n$ be the set of $n$-tuples of strictly positive integers.

For $u=(u_1,\cdots ,u_n)$ and $v=(v_1,\cdots ,v_n)$ two elements of $E_n$, we define:

• the Sum Of Products of $u$ and $v$, denoted by $⟨u,v⟩$, as the sum ${\displaystyle \sum _{i=1}^n{u}_i{v}_i}$;
• the Product Of Sums of $u$ and $v$, denoted by $u\star v$, as the product ${\displaystyle \prod _{i=1}^n(u_i+v_i)}$.

Let $R_n(M)$ be the sum of $u\star v$ over all ordered pairs $(u,v)$ in $E_n$ such that $⟨u,v⟩=M$.
For example: $R_1(10)=36$, $R_2(100)=1873044$, $R_2(100!)\equiv 446575636mod{10}^9+7$.

Find $R_6(10000!)$. Give your answer modulo ${10}^9+7$.