Minimum Limit of Balls in a Bag

Medium

Given an array nums of bag sizes and an integer target (the maximum number of split operations allowed), each operation splits one bag into two smaller non-negative bags. Return the minimum possible penalty, where the penalty is the maximum number of balls in any bag after all operations.

Example 1

Input:  nums = [9], target = 2
Output: 3

Example 2

Input:  nums = [2,4,8,2], target = 4
Output: 2

Constraints

• 1 <= nums.length <= 10^5
• 1 <= nums[i] <= 10^9
• 1 <= target <= 10^9