#223EasySimulation· Round-Robin Queue

Ticket Counter Rounds

At a concert box office the line is served in rounds. The person at the front buys exactly **one** ticket, which takes one second, and then either leaves (if they have bought everything they wanted) or goes to the back of the line to wait for another turn. `tickets[i]` is how many tickets the person initially standing at position `i` wants. Return the number of seconds that pass until the person initially at position `k` buys their last ticket. Counting starts at 0 and includes the second in which that last ticket is bought.

Input format

`tickets`: an array of positive integers; `k`: a position in the line.

Output format

An integer: the total seconds until person `k` is finished.

Examples

Input: tickets = [2, 3, 2], k = 2

Output: 6

Round 1 serves everybody once (3 seconds), leaving 1, 2, 1. Round 2 serves person 0 (finished), person 1, then person 2, who finishes at second 6.

Input: tickets = [5, 1, 1, 1], k = 0

Output: 8

Person 0 needs 5 turns. Others leave after round 1, so the line shrinks: 4 seconds in round 1, then person 0 buys alone for 4 more seconds, giving 8.

Input: tickets = [1], k = 0

Output: 1

A single person with a single ticket takes one second.

Constraints

1 <= tickets.length <= 10^4
1 <= tickets[i] <= 10^4
0 <= k < tickets.length
The answer is at most 10^8.

#simulation
#queue
#math
#round-robin