1760 - Minimum Limit of Balls in a Bag\.

Medium

You are given an integer array nums where the <code>i^th</code> 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.

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:

• <code>1 <= nums.length <= 10⁵</code>

• <code>1 <= maxOperations, numsi<= 10⁹</code>