what is the fastest way to randomly select some numbers in a range that contains a given set of numbers?

Here is the function I want

random_select(contain_list, ttl_num, sample_num)

There're ttl_num integers from 0 to ttl_num-1 to select from, I want to return a list of sample_num integers, where numbers provided in contain_list have to be in the list, and other numbers are selected randomly.

I have to do this query very often, every time with a different contain_list, but ttl_num, sample_num and the length of contain_list are the same for all the queries.

Currently what I'm doing is, first generate a set of ttl_num integers, subtract contain_list from the set, randomly select some numbers with no replacement from the rest, then concatenate it with the contain_list to get the result.

I believe this is not the fastest way, any better thoughts?

It's okay to use global variables if needed.