Find top-K frequent values with tiebreaks

Given an integer array nums and an integer k, return the k values with highest frequency. If multiple values share the same frequency, break ties by ( 1) smaller numeric value, then ( 2) earlier first-occurrence index. The array can contain up to 10^6 elements. Provide an algorithm faster than O(n log n) (e.g., O(n) or O(n log k)), justify correctness under the tie rules, and discuss trade-offs among bucket counting, heaps, and selection.