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.
<ul> <li>For example, a bag of <code>5</code> balls can become two new bags of <code>1</code> and <code>4</code> balls, or two new bags of <code>2</code> and <code>3</code> balls.</li> </ul> </li>
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 an you should return 2.
Example 3:
Input: nums = [7,17], maxOperations = 2 Output: 7
Constraints:
1 <= nums.length <= 1051 <= maxOperations, nums[i] <= 109