You are given an array of integers strength of length n, representing the strengths of n locks, and an integer k.

You start with an initial energy of $0$ and a multiplier factor $X = 1$. In each minute, your energy increases by $X$.

To break a lock with strength strength[i], your current accumulated energy must be greater than or equal to strength[i]. Once a lock is broken:

• Your energy resets to $0$.

• The multiplier factor $X$ increases by k (that is, $X$ becomes $X +$ k).

You may break the locks in any order. The time in minutes required to break a lock of strength $S$ with a current multiplier $X$ is $\lceil S / X \rceil$.

Return the minimum total time in minutes required to break all n locks.

Constraints:

• n == strength.length

• $1 \leq n \leq 8$

• $1 \leq$ k $\leq 10$

• $1 \leq$ strength[i] $\leq 10^6$

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.