You are given an array nums of positive integers. In one operation, you may choose any element from nums and replace it with exactly half of its value.

Return the minimum number of operations required to reduce the total sum of nums by at least half of its initial sum.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^7$

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.