Minimum Limit of Balls in a Bag

You are given an integer array `nums` where the `ith` bag contains `nums[i]` balls. You are also given an integer `maxOperations`. You can perform the following operation at most `maxOperations` times: - Take any bag of balls and divide it into two new bags with a **positive **number of balls. - For example, a bag of `5` balls can become two new bags of `1` and `4` balls, or two new bags of `2` and `3` balls. Your penalty is the **maximum** number of balls in a bag. You want to **minimize** your penalty after the operations. Return _the minimum possible penalty after performing the operations_.   **Example 1:** **Input:** nums = [9], maxOperations = 2 **Output:** 3 **Explanation:** - Divide the bag with 9 balls into two bags of sizes 6 and 3. [**9**] -> [6,3]. - Divide the bag with 6 balls into two bags of sizes 3 and 3. [**6**,3] -> [3,3,3]. The bag with the most number of balls has 3 balls, so your penalty is 3 and you should return 3. ``` **Example 2:** **Input:** nums = [2,4,8,2], maxOperations = 4 **Output:** 2 **Explanation:** - Divide the bag with 8 balls into two bags of sizes 4 and 4. [2,4,**8**,2] -> [2,4,4,4,2]. - Divide the bag with 4 balls into two bags of sizes 2 and 2. [2,**4**,4,4,2] -> [2,2,2,4,4,2]. - Divide the bag with 4 balls into two bags of sizes 2 and 2. [2,2,2,**4**,4,2] -> [2,2,2,2,2,4,2]. - Divide the bag with 4 balls into two bags of sizes 2 and 2. [2,2,2,2,2,**4**,2] -> [2,2,2,2,2,2,2,2]. The bag with the most number of balls has 2 balls, so your penalty is 2, and you should return 2. ```   **Constraints:** - `1 <= nums.length <= 105` - `1 <= maxOperations, nums[i] <= 109`