You are given an integer array nums and an integer k.

Initially, you have k units of resources and must process every element in nums sequentially from index $0$ to index nums.length $- 1$.

To process an element nums[i], you must have at least nums[i] units of resources. If your current resources are strictly less than nums[i], you must perform replenishment operations until you have enough resources:

• Each operation adds k units to your available resources.

• The $m$th operation performed overall incurs a cost of $m$, where $m \geq 1$.

Processing nums[i] consumes nums[i] units of resources.

Return the minimum total cost required to process all elements in nums.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^9$

• $1 \leq$ k $\leq 10^9$

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.