Time Needed to Buy Tickets

There are n people in a line to buy tickets. Each person wants to buy a certain number of tickets, represented by tickets[i]. The ticket counter sells one ticket at a time, and each person takes 1 second to buy one ticket. After buying a ticket, if a person still needs more tickets, they go to the back of the line.

You are the person at position k (0-indexed). Calculate how many seconds it takes for you to finish buying all your tickets.

Input

tickets: a list of integers where tickets[i] is the number of tickets person i wants to buy
k: an integer representing your position in line (0-indexed)

Output

An integer representing the total time in seconds for person k to finish buying all their tickets

Examples

####Example 1:

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

Output: 6

Explanation: Keep people fixed as indices 0, 1, 2. We only track their remaining tickets.

Start: remaining = [2, 3, 2]
Time 1: Person 0 buys, remaining = [1, 3, 2]
Time 2: Person 1 buys, remaining = [1, 2, 2]
Time 3: Person 2 (you) buys, remaining = [1, 2, 1]
Time 4: Person 0 buys, remaining = [0, 2, 1]
Time 5: Person 1 buys, remaining = [0, 1, 1]
Time 6: Person 2 (you) buys and finishes, remaining = [0, 1, 0]

Example 2:

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

Output: 8

Explanation:

You need 5 tickets and are at position 0
After the first round, everyone else is done (they only needed 1 ticket each)
You still need 4 tickets: times 5, 6, 7, 8

Example 3:

Input: tickets = [1], k = 0

Output: 1

Explanation: Only you in line, takes 1 second to buy your ticket