777 . Investment
Description
John never knew he had a grand-uncle, until he received the notary’s letter. He learned that
his late grand-uncle had gathered a lot of money, somewhere in South-America, and that
John was the only inheritor.
John did not need that much money for the moment. But he realized that it would be a
good idea to store this capital in a safe place, and have it grow until he decided to retire. The
bank convinced him that a certain kind of bond was interesting for him.
This kind of bond has a fixed value, and gives a fixed amount of yearly interest, payed
to the owner at the end of each year. The bond has no fixed term. Bonds are available in
different sizes. The larger ones usually give a better interest. Soon John realized that the
optimal set of bonds to buy was not trivial to figure out. Moreover, after a few years his
capital would have grown, and the schedule had to be re-evaluated.
Assume the following bonds are available:
With a capital of €10 000 one could buy two bonds of €4 000, giving a yearly interest of
€800. Buying two bonds of €3 000, and one of €4 000 is a better idea, as it gives a yearly
interest of €900. After two years the capital has grown to €11 800, and it makes sense to sell
a €3 000 one and buy a €4 000 one, so the annual interest grows to €1 050. This is where this
story grows unlikely: the bank does not charge for buying and selling bonds. Next year the
total sum is €12 850, which allows for three times €4 000, giving a yearly interest of €1 200.
Here is your problem: given an amount to begin with, a number of years, and a set of
bonds with their values and interests, find out how big the amount may grow in the given
period, using the best schedule for buying and selling bonds.
Input Format
The first line contains a single positive integer N which is the number of test cases. The test
cases follow.
The first line of a test case contains two positive integers: the amount to start with (at
most €1 000 000), and the number of years the capital may grow (at most 40).
The following line contains a single number: the number d (1 ≤ d ≤ 10) of available
bonds.
The next d lines each contain the description of a bond. The description of a bond consists
of two positive integers: the value of the bond, and the yearly interest for that bond. The
value of a bond is always a multiple of €1 000. The interest of a bond is never more than
10% of its value.
Output Format
For each test case, output – on a separate line – the capital at the end of the period, after an
optimal schedule of buying and selling.
Sample Input 1
1
10000 4
2
4000 400
3000 250
Sample Output 1
14050
Hints
Problem Source
Migrated from old NTUJ.
nwerc2004
Subtasks
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