There are n people in a line queuing to buy tickets, where the 0th person is at the front of the line and the (n - 1)th person is at the back of the line.
You are given a 0-indexed integer array tickets of length n where the number of tickets that the ith person would like to buy is tickets[i].
Each person takes exactly 1 second to buy a ticket. A person can only buy 1 ticket at a time and has to go back to the end of the line (which happens instantaneously) in order to buy more tickets. If a person does not have any tickets left to buy, the person will leave the line.
Return the time taken for the person initially at position k (0-indexed) to finish buying tickets.
Example 1:
Input: tickets = [2,3,2], k = 2
Output: 6
Explanation:
- The queue starts as [2,3,2], where the kth person is underlined.
- After the person at the front has bought a ticket, the queue becomes [3,2,1] at 1 second.
- Continuing this process, the queue becomes [2,1,2] at 2 seconds.
- Continuing this process, the queue becomes [1,2,1] at 3 seconds.
- Continuing this process, the queue becomes [2,1] at 4 seconds. Note: the person at the front left the queue.
- Continuing this process, the queue becomes [1,1] at 5 seconds.
- Continuing this process, the queue becomes [1] at 6 seconds. The kth person has bought all their tickets, so return 6.
Example 2:
Input: tickets = [5,1,1,1], k = 0
Output: 8
Explanation:
- The queue starts as [5,1,1,1], where the kth person is underlined.
- After the person at the front has bought a ticket, the queue becomes [1,1,1,4] at 1 second.
- Continuing this process for 3 seconds, the queue becomes [4] at 4 seconds.
- Continuing this process for 4 seconds, the queue becomes [] at 8 seconds. The kth person has bought all their tickets, so return 8.
Constraints:
n == tickets.length1 <= n <= 1001 <= tickets[i] <= 1000 <= k < n