2332\. The Latest Time to Catch a Bus

Medium

You are given a **0-indexed** integer array `buses` of length `n`, where `buses[i]` represents the departure time of the <code>i<sup>th</sup></code> bus. You are also given a **0-indexed** integer array `passengers` of length `m`, where `passengers[j]` represents the arrival time of the <code>j<sup>th</sup></code> passenger. All bus departure times are unique. All passenger arrival times are unique.

You are given an integer `capacity`, which represents the **maximum** number of passengers that can get on each bus.

The passengers will get on the next available bus. You can get on a bus that will depart at `x` minutes if you arrive at `y` minutes where `y <= x`, and the bus is not full. Passengers with the **earliest** arrival times get on the bus first.

Return _the latest time you may arrive at the bus station to catch a bus_. You **cannot** arrive at the same time as another passenger.

**Note:** The arrays `buses` and `passengers` are not necessarily sorted.

**Example 1:**

**Input:** buses = [10,20], passengers = [2,17,18,19], capacity = 2

**Output:** 16

**Explanation:**

The 1<sup>st</sup> bus departs with the 1<sup>st</sup> passenger.

The 2<sup>nd</sup> bus departs with you and the 2<sup>nd</sup> passenger.

Note that you must not arrive at the same time as the passengers, which is why you must arrive before the 2<sup>nd</sup> passenger to catch the bus.

**Example 2:**

**Input:** buses = [20,30,10], passengers = [19,13,26,4,25,11,21], capacity = 2

**Output:** 20

**Explanation:**

The 1<sup>st</sup> bus departs with the 4<sup>th</sup> passenger.

The 2<sup>nd</sup> bus departs with the 6<sup>th</sup> and 2<sup>nd</sup> passengers.

The 3<sup>rd</sup> bus departs with the 1<sup>s</sup><sup>t</sup> passenger and you. 

**Constraints:**

*   `n == buses.length`
*   `m == passengers.length`
*   <code>1 <= n, m, capacity <= 10<sup>5</sup></code>
*   <code>2 <= buses[i], passengers[i] <= 10<sup>9</sup></code>
*   Each element in `buses` is **unique**.
*   Each element in `passengers` is **unique**.