<p>You are given a <strong>0-indexed</strong> integer array <code>buses</code> of length <code>n</code>, where <code>buses[i]</code> represents the departure time of the <code>i<sup>th</sup></code> bus. You are also given a <strong>0-indexed</strong> integer array <code>passengers</code> of length <code>m</code>, where <code>passengers[j]</code> 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.</p>

<p>You are given an integer <code>capacity</code>, which represents the <strong>maximum</strong> number of passengers that can get on each bus.</p>

<p>When a passenger arrives, they will wait in line for the next available bus. You can get on a bus that departs at <code>x</code> minutes if you arrive at <code>y</code> minutes where <code>y &lt;= x</code>, and the bus is not full. Passengers with the <strong>earliest</strong> arrival times get on the bus first.</p>

<p>More formally when a bus arrives, either:</p>

<ul>
	<li>If <code>capacity</code> or fewer passengers are waiting for a bus, they will <strong>all</strong> get on the bus, or</li>
	<li>The <code>capacity</code> passengers with the <strong>earliest</strong> arrival times will get on the bus.</li>
</ul>

<p>Return <em>the latest time you may arrive at the bus station to catch a bus</em>. You <strong>cannot</strong> arrive at the same time as another passenger.</p>

<p><strong>Note: </strong>The arrays <code>buses</code> and <code>passengers</code> are not necessarily sorted.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> buses = [10,20], passengers = [2,17,18,19], capacity = 2
<strong>Output:</strong> 16
<strong>Explanation:</strong> Suppose you arrive at time 16.
At time 10, the first bus departs with the 0<sup>th</sup> passenger. 
At time 20, the second bus departs with you and the 1<sup>st</sup> passenger.
Note that you may not arrive at the same time as another passenger, which is why you must arrive before the 1<sup>st</sup> passenger to catch the bus.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> buses = [20,30,10], passengers = [19,13,26,4,25,11,21], capacity = 2
<strong>Output:</strong> 20
<strong>Explanation:</strong> Suppose you arrive at time 20.
At time 10, the first bus departs with the 3<sup>rd</sup> passenger. 
At time 20, the second bus departs with the 5<sup>th</sup> and 1<sup>st</sup> passengers.
At time 30, the third bus departs with the 0<sup>th</sup> passenger and you.
Notice if you had arrived any later, then the 6<sup>th</sup> passenger would have taken your seat on the third bus.</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == buses.length</code></li>
	<li><code>m == passengers.length</code></li>
	<li><code>1 &lt;= n, m, capacity &lt;= 10<sup>5</sup></code></li>
	<li><code>2 &lt;= buses[i], passengers[i] &lt;= 10<sup>9</sup></code></li>
	<li>Each element in <code>buses</code> is <strong>unique</strong>.</li>
	<li>Each element in <code>passengers</code> is <strong>unique</strong>.</li>
</ul>

#
'''
cap = 2
[2,8]
   ^
[1,2,4,5,6]
   m s
         i  
-1
-1

'''
from typing import List
class Solution:
    def latestTimeCatchTheBus(self, buses: List[int], passengers: List[int], capacity: int) -> int:
        buses = sorted(buses)
        passengers = sorted(passengers)
        passengers_lookup = set(passengers)
        p_i = 0
        p_s = 0
        cur_min = -1
        last_time = -1
        for b_i in range(len(buses)):
            print('BUS',b_i)
            cur_capacity = capacity
            p_i = p_s
            while p_i < len(passengers) and passengers[p_i] <= buses[b_i] and cur_capacity:
                cur_capacity -= 1
                p_i += 1
            
            if cur_capacity != 0:
                last_person_time = buses[b_i] + 1
            else:
                last_person_time = passengers[p_i - 1]
            print(last_person_time, cur_min, cur_capacity)
            for time in range(last_person_time - 1, cur_min, -1):
                if time not in passengers_lookup:
                    last_time = max(time, last_time)
                    break
            cur_min = 0
            p_s = p_i
        return last_time
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