Consider the set $S$ of all possible products of $n$ positive integers not exceeding $m$, that is
$S=\{x_1{x}_2\cdots x_n\mid 1\le x_1,x_2,\dots ,x_n\le m\}$.
Let $F(m,n)$ be the number of the distinct elements of the set $S$.
For example, $F(9,2)=36$ and $F(30,2)=308$.

Find $F(30,10001)mod1000000007$.