Find a linear bounded automaton that accepts the language $L = { a^{n!} : n geq 0 }$

I need to construct linear bounded automaton for the language $L = { a^{n!} : n geq 0 }$. I know how LBA functions, however, I don’t have a thought how it can check the n! that to in the power of a. I might want to hear a few suggestions, as I am experiencing difficulty in developing the specific LBA for it.