You are given a positive integer k. You start with an array nums = [$1$].

In one operation, you can perform either of the following actions:

1. Choose an element in nums and increment its value by $1$.

2. Select an element in nums and append a duplicate copy of it to nums.

Return the minimum number of operations required to make the sum of the elements in nums greater than or equal to k.

Constraints:

• $1 \leq$ k $\leq 10^5$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.