Propose a data structure to use for the following situation. Justify your

choices. You do not need to give complete code, but it should be clear

how your solution is intended to work. You can use all data structures and

operations on these data structures that have been described in lectures as

"black$-$box" without giving an implementation.

You want to write a simple "unpaid bill manager". New bills arrive

frequently. For each bill you also have a deadline for paying the bill. On

arrival of a bill you want to add the new bill to your structure. You always

want to pay the bill with the earliest deadline.

You also may want to know the total amount to pay for all bills with

deadlines less than or equal to a time $T.$ That is$,$ you want to efficiently

query your data structure to return the total amount to pay up to any time

$T.$

You may assume that the bill deadlines are integers $($day numbers$),$ and

at most one bill will arrive with a deadline on any day.

Your "unpaid bill manager" should be able to:

Add a new unpaid bill to your structure. $($Note that the deadlines of

new bills are not necessarily in time order.$)$

Find the bill with the earliest deadline, output it$,$ and delete it from

the structure.

Calculate the total cost of bills with deadlines up to $T,$ for any time

$T.$

What is the time required for the three basic operations $($add a new bill,

find the next bill to pay, and calculate total amount of bills up to time $T?$