Least number divisible by each number of a sequence

Given two integers $m>0$ and $n>0$, let $L(m,n)$ be the number of sequences which satisfy the following properties:

• Each number in the sequence is a natural number.
• The least number divisible by each number of the sequence is $m$.
• The length of the sequence is $n$.
• Any two adjacent terms in the sequence are co-prime.

For example, $L(4,3)=6$, there are only 6 co-prime sequences: {1,1,4}, {1,4,1}, {2,1,4}, {4,1,1}, {4,1,2}, and {4,1,4}.

You are given $L(10!,10)\equiv 800548088(\mathrm{mod}1000000007)$ and $L(100!,100)\equiv 73129372(\mathrm{mod}1000000007)$

Find $L({10}^{12}!,{10}^{12})mod1000000007$