There are n people in a line queuing to buy tickets, where the person at index 0 is at the front and the person at index n - 1 is at the back.

You are given a 0-indexed integer array tickets of length n, where tickets[i] represents the number of tickets the person at index i wants to buy.

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.

You are also given an integer k. Return the total time in seconds it takes for the person initially at index k to finish buying all their tickets.

Example 1:

Input: tickets = [2,5,2], k = 2
Output: 6
Explanation:
• The queue starts as [2,5,2], and the target person is initially at index k = 2.
• After the person at the front has bought a ticket, the queue becomes [5,2,1] at 1 second.
• Continuing this process, the queue becomes [2,1,4] at 2 seconds.
• Continuing this process, the queue becomes [1,4,1] at 3 seconds.
• Continuing this process, the queue becomes [4,1] at 4 seconds. Note: the person who started at index 0 has finished and leaves the queue.
• Continuing this process, the queue becomes [1,3] at 5 seconds.
• Continuing this process, the queue becomes [3] at 6 seconds. The target person has bought all their tickets, so return 6.

Example 2:

Input: tickets = [6,1,1,1], k = 0
Output: 9
Explanation:
The queue starts as [6,1,1,1], and the target person is initially at index k = 0.
After the person at the front has bought a ticket, the queue becomes [1,1,1,5] at 1 second.
Continuing this process for 3 seconds, the queue becomes [5] at 4 seconds.
Continuing this process for 5 seconds, the queue becomes [] at 9 seconds. The kth person has bought all their tickets, so return 9.

Example 3:

Input: tickets = [3,5,7], k = 1
Output: 12
Explanation:
The queue starts as [3,5,7], and the target person is initially at index k = 1.
After the person at the front has bought a ticket, the queue becomes [5,7,2] at 1 second.
Continuing this process, the queue becomes [7,2,4] at 2 seconds.
Continuing this process, the queue becomes [2,4,6] at 3 seconds.
Continuing this process, the queue becomes [4,6,1] at 4 seconds.
Continuing this process, the queue becomes [6,1,3] at 5 seconds.
Continuing this process, the queue becomes [1,3,5] at 6 seconds.

Continuing this process, the queue becomes [3,5] at 7 seconds. Note: the person who started at index 0 has finished and leaves the queue.
Continuing this process, the queue becomes [5,2] at 8 seconds.
Continuing this process, the queue becomes [2,4] at 9 seconds.
Continuing this process, the queue becomes [4,1] at 10 seconds.
Continuing this process, the queue becomes [1,3] at 11 seconds.
Continuing this process, the queue becomes [3] at 12 seconds. 
The target person has bought all their tickets, so return 12.

Constraints

n == tickets.length
1 <= n <= 100
1 <= tickets[i] <= 100
0 <= k < n

11. Time Required to Buy Tickets