Assume you are given a list of real numbers. Your goal is to determine if there is a pair of numbers in this list whose product is exactly 1. What is the fastest deterministic algorithm you can devise to solve this problem? Assume that you can do exact multiplication and division in O(1) time. Now suppose you have access to a hash table. Can you use it to get a faster algorithm? What properties would you like the hash function to have? PLEASE EXPLAIN IT CLEARLY.