You are given a positive integer hp and two positive 1-indexed integer arrays damage and requirement.

There is a dungeon with n trap rooms numbered from 1 to n. Entering room i reduces your health points by damage[i]. After that reduction, if your remaining health points are at least requirement[i], you earn 1 point for that room.

Let score(j) be the number of points you get if you start with hp health points and enter the rooms j, j + 1, ..., n in this order.

Return the integer score(1) + score(2) + ... + score(n), the sum of scores over all starting rooms.

Note: You cannot skip rooms. You can finish your journey even if your health points become non-positive.

Input: hp = 11, damage = [3,6,7], requirement = [4,2,5]

Output: 3

Explanation:

score(1) = 2, score(2) = 1, score(3) = 0. The total score is 2 + 1 + 0 = 3.

As an example, score(1) = 2 because you get 2 points if you start from room 1.

You start with 11 health points.
Enter room 1. Your health points are now 11 - 3 = 8. You get 1 point because 8 >= 4.
Enter room 2. Your health points are now 8 - 6 = 2. You get 1 point because 2 >= 2.
Enter room 3. Your health points are now 2 - 7 = -5. You do not get any points because -5 < 5.

Input: hp = 2, damage = [10000,1], requirement = [1,1]

Output: 1

Explanation:

score(1) = 0, score(2) = 1. The total score is 0 + 1 = 1.

score(1) = 0 because you do not get any points if you start from room 1.

You start with 2 health points.
Enter room 1. Your health points are now 2 - 10000 = -9998. You do not get any points because -9998 < 1.
Enter room 2. Your health points are now -9998 - 1 = -9999. You do not get any points because -9999 < 1.

score(2) = 1 because you get 1 point if you start from room 2.

You start with 2 health points.
Enter room 2. Your health points are now 2 - 1 = 1. You get 1 point because 1 >= 1.