You are given an integer hp representing your initial health points, and two integer arrays damage and requirement, each of length n.

A dungeon contains n rooms numbered from $0$ to n $- 1$. You can choose to start a run from any room i ($0 \le$ i $<$ n) with an initial health of hp points and visit the rooms sequentially from room i to room n $- 1$.

In each run starting from room i:

• When you enter room j (i $\le$ j $<$ n), your health points decrease by damage[j].

• If your remaining health points after taking damage are greater than or equal to requirement[j], you earn $1$ point.

Let score(i) be the total points earned when starting the run from room i.

Return the total score obtained by summing score(i) across all possible starting rooms i from $0$ to n $- 1$.

Constraints:

• $1 \leq$ hp $\leq 10^9$

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

• $1 \leq$ damage[i], requirement[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.