Given an integer array nums and an integer k, return true if nums has a subarray of at least two elements whose sum is a multiple of k.

Focus on developing an efficient algorithm to solve the problem, considering both time and space complexity. Start by discussing the concept of prefix sums and how they can be utilized to track cumulative sums while iterating through the array. Emphasize the importance of using a hash map to store previously seen remainders when dividing by k, as this will help identify subarrays whose sums are multiples of k. Be prepared to explain edge cases, such as when k is zero or when the array contains negative numbers, and how these cases affect your approach. Finally, ensure you articulate your thought process clearly, as the interviewer will be interested in how you arrive at your solution.