You are given a $0$ indexed integer array buses of length n, where buses[i] represents the departure time of the $i^{ ext{th}}$ bus. You are also given a $0$ indexed integer array passengers of length m, where passengers[j] represents the arrival time of the $j^{ ext{th}}$ passenger. In addition, you are given an integer capacity, which denotes the maximum number of passengers that can board any single bus.

Passengers board buses in order of their arrival time. Each passenger will board the earliest departing bus that still has available capacity and departs at or after their arrival time.

You want to catch a bus. You are allowed to board a bus if there is remaining capacity at its departure time, but you cannot arrive at the same time as any other passenger.

Return the latest time you can arrive to catch a bus.

Note: You cannot arrive at the same time as another passenger, and you must arrive at or before the departure time of the bus you board.

Constraints:

• n $==$ buses.length

• m $==$ passengers.length

• $1 \leq$ n, m, capacity $\leq 10^5$

• $2 \leq$ buses[i], passengers[i] $\leq 10^9$

• Each element in buses is unique.

• Each element in passengers is unique.

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.