You are given an integer array nums and two integers k and mul.

You need to select exactly k elements from nums and choose the order in which to process them.

For each selected element, you can perform one of the following operations:

• Multiply the element by the current value of mul, add the resulting product to the total sum, and then decrease mul by $1$.

• Add the element directly to the total sum without modifying mul.

Return the maximum possible total sum that can be obtained after processing all k selected elements.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^5$

• $1 \leq$ k $\leq$ nums.length

• $1 \leq$ mul $\leq 10^5$

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.