Problem C: Exact Change
When travelling to remote locations, it is often helpful to bring
cash, in case you want to buy something from someone who does not
accept credit or debit cards. It is also helpful to bring a variety
of denominations in case the seller does not have change. Even so,
you may not have the exact amount, and will have to pay a little
bit more than full price. The same problem can arise even in urban
locations, for example with vending machines that do not return change.
- Seller: That will be fourteen dollars.
- Buyer: Here's a twenty.
- Seller: Sorry, I don't have any change.
- Buyer: OK, here's a ten and a five. Keep the change.
Of course, you would like to minimize the amount you pay
(though you must pay at least as much as the value of the item).
Moreover, while paying the minimum amount, you would like to minimize
the number of coins or bills that you pay out.
The first line of input contains one integer specifying the number of
test cases to follow. Each test case begins with a line containing
an integer, the price in cents of the item you would like to buy.
The price will not exceed 10 000 cents (i.e., $100).
The following line contains a single integer n, the number of bills
and coins that you have. The number n is at most 100.
The following n lines
each contain one integer, the value in cents of each bill or coin
that you have. Note that the denominations can be any number of
cents; they are not limited to the values of coins and bills that
we usually use in Canada. However, no bill or coin will have a value
greater than 10 000 cents ($100).
The total value of your bills and coins
will always be equal to or greater than the price of the item.
For each test case, output a single line containing two integers:
the total amount paid (in cents), and the total number of coins and
Output for Sample Input