Implement streaming k-way merge with constraints

Implement a function merge_k(iterators, N) that returns the first N items of the global ascending order from k sorted, potentially unbounded iterators of integers. Constraints: iterators may block, memory must be O(k), and duplicates must be preserved but made stable by source index (stable tie-breaker). Specify time complexity, show how you would handle iterator exhaustion, and discuss how to add deduplication (unique-only) without increasing asymptotic complexity. Provide unit tests that cover k=1, empty streams, large N, and pathological inputs (e.g., one iterator far slower than the rest).