Maximize protected population and bitwise AND

You are given two independent coding problems. ## Problem 1: Maximize protected population after moving units There are **n** cities in a line (indexed **1..n**). City *i* has population `population[i]`. Initially, some cities contain **one** security unit and others contain **none**. You are given an array `unit[i]` where: - `unit[i] = 1` means city *i* initially has one unit - `unit[i] = 0` means it has no unit You may **reassign** units using these rules: - Each security unit may move **at most one city to the left** (from city *i* to city *i-1*). - Each security unit can be moved **at most once** (so it either stays, or moves left by 1). - A unit in city **1** cannot move left. - After all moves, a city is considered **protected** if it contains **at least one** unit (multiple units in one city are allowed but do not add extra benefit). **Goal:** After performing moves, maximize the **total population of protected cities**. **Task:** Return the maximum possible protected population sum. --- ## Problem 2: Maximize bitwise AND after at most k increments You are given an array `customer_rating` of length **n** (assume all values are non-negative integers). You may perform the following operation **at most k times** in total: - Choose any index `i` and do `customer_rating[i] += 1`. After performing up to **k** increments, you must: - Choose **exactly m** elements from the final array (any indices you want), and - Compute the **bitwise AND** of those **m** chosen values. Call the result `new_rating`. **Goal:** Maximize `new_rating`. **Task:** Return the maximum possible `new_rating` achievable with at most `k` total `+1` operations.