You are given an integer power and two integer arrays, damage and health, both of length $n$.

Bob is facing $n$ enemies. The $i^{ ext{th}}$ enemy has health[i] health and deals damage[i] points of damage to Bob every second.

Every second, Bob can choose one enemy to attack, reducing their health by power. An enemy is defeated once their health reaches $0$ or less, after which they can no longer inflict damage. During each second, all surviving enemies deal damage to Bob simultaneously.

Return the minimum total damage inflicted on Bob before all enemies are eliminated.

Constraints:

• $1 \leq$ power $\leq 10^4$

• $1 \leq n ==$ damage.length $==$ health.length $\leq 10^5$

• $1 \leq$ damage[i], health[i] $\leq 10^4$

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.