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Determine if a multiple-sum subarray exists

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This interview question evaluates algorithm design, data structures, correctness, complexity, edge cases, and implementation details in a realistic interview setting. A strong answer for Determine if a multiple-sum subarray exists states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Given an integer array nums and an integer k, determine whether there exists a contiguous subarray of length at least 2 whose sum is divisible by k; return true if such a subarray exists, otherwise false. If k = 0, interpret the requirement as finding a length ≥2 subarray with sum exactly 0. Explain your approach and analyze time and space complexity. Follow-up: how would you adapt your solution to a streaming setting where nums arrives incrementally?