ATM queue exit order

There are n people waiting in a single line at an ATM. They are numbered 1 to n from the front of the line to the back.

You are given an integer array amounts, where amounts[i] is the total money that person i + 1 wants to withdraw, and an integer k, the most the ATM pays out in one turn.

The line works like this:

• The person at the front steps up and withdraws min(remaining, k), where remaining is what they still need.
• If they now have their full amount, they leave the line.
• Otherwise they go to the back of the line and wait for another turn.

Return a list of the people's numbers in the order in which they leave the line.

Implement atm_queue(amounts: list[int], k: int) -> list[int].

Constraints

• 0 <= n <= 10^5
• 1 <= amounts[i] <= 10^9
• 1 <= k <= 10^9

Example 1

amounts = [5, 1, 4], k = 2
Output: [2, 3, 1]

Person 1 takes 2 and goes to the back (needs 3). Person 2 takes 1 and leaves. Person 3 takes 2 and goes to the back (needs 2). Person 1 takes 2 (needs 1). Person 3 takes 2 and leaves. Person 1 takes 1 and leaves.

Example 2

amounts = [10, 10, 10], k = 4
Output: [1, 2, 3]

Everyone needs three turns, so they finish in the same round in their original order.