Minimum Cost to Hire K Workers

There are `n` workers. You are given two integer arrays `quality` and `wage` where `quality[i]` is the quality of the `ith` worker and `wage[i]` is the minimum wage expectation for the `ith` worker. We want to hire exactly `k` workers to form a **paid group**. To hire a group of `k` workers, we must pay them according to the following rules: - Every worker in the paid group must be paid at least their minimum wage expectation. - In the group, each worker's pay must be directly proportional to their quality. This means if a worker’s quality is double that of another worker in the group, then they must be paid twice as much as the other worker. Given the integer `k`, return _the least amount of money needed to form a paid group satisfying the above conditions_. Answers within `10-5` of the actual answer will be accepted.   **Example 1:** **Input:** quality = [10,20,5], wage = [70,50,30], k = 2 **Output:** 105.00000 **Explanation:** We pay 70 to 0th worker and 35 to 2nd worker. ``` **Example 2:** **Input:** quality = [3,1,10,10,1], wage = [4,8,2,2,7], k = 3 **Output:** 30.66667 **Explanation:** We pay 4 to 0th worker, 13.33333 to 2nd and 3rd workers separately. ```   **Constraints:** - `n == quality.length == wage.length` - `1 <= k <= n <= 104` - `1 <= quality[i], wage[i] <= 104`