Find Weekly Deployment Windows Across Time Zones

## Problem A week is a repeating timeline of `10080` minutes. Teams define local-time intervals that either allow or freeze deployments, together with fixed UTC offsets. Find the first `k` non-overlapping UTC deployment windows after a lead-time boundary. ## Function Contract Implement `deployment_windows(utc_now, lead_time, min_duration, k, rules)` and return half-open absolute UTC intervals `[start, end]`. Each rule is `[kind, local_start, local_end, offset]`. ## Rules - `kind` is `"ALLOW"` or `"FREEZE"`; local intervals are half-open and may wrap across the weekly boundary. - At absolute UTC minute `u`, a rule is active when `(u + offset) mod 10080` lies in its local interval. - A minute is deployable when at least one `ALLOW` rule is active and no `FREEZE` rule is active. - No returned start may be earlier than `utc_now + lead_time`, and every window has exactly `min_duration` consecutive deployable minutes. - Split a longer deployable span into adjacent windows of length `min_duration`; discard a trailing fragment that is too short. - Search the half-open horizon from the earliest start through three complete weeks later, and return fewer than `k` windows if necessary. ## Constraints - `0 <= utc_now, lead_time <= 10^9`. - `1 <= min_duration <= 10080`. - `1 <= k <= 10000`. - `1 <= len(rules) <= 10000`. - Offsets are integer minutes in `[-1440, 1440]`; local endpoints are in `[0, 10080]`. ## Examples ```text utc_now = 10070 lead_time = 20 min_duration = 30 k = 2 rules = [["ALLOW", 0, 120, 60]] output = [[10090,10120],[20100,20130]] ``` The lead-time boundary is `10090`. With the positive offset, the current deployable span is `[10090, 10140)`, which contains one 30-minute window and a 20-minute trailing fragment. The fragment is discarded. The underlying weekly allow interval next recurs as the UTC span `[20100, 20220)`, whose first 30-minute window is `[20100, 20130)`, providing the second requested window.