MINVEST - Investment Money

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:

Value Annual interest
4000 400
3000 250

With a capital of 10 000$ one could buy two bonds of 4000$, giving a yearly interest of 800$. Buying two bonds of 3000$, and one of 4000$ is a better idea, as it gives a yearly interest of e900. After two years the capital has grown to 11800$, and it makes sense to sell a 3000$ one and buy a 4000$ one, so the annual interest grows to 1050$.

This iswhere this story grows unlikely: the bank does not charge for buying and selling bonds. Next year the total sum is 12850$, which allows for three times 4000$, giving a yearly interest of 1200$. 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.



The first line contains a single positive integer N which is the number of test cases. The first line of a test case contains two positive integers: the amount to start with (at most 1000 000$), and the number of years the capital may grow (at most 40). The following line contains a single number: the number d (1 ≤ d ≤ 10) of available bonds. The next d lines each contain the description of a bond. The description of a bond consists of two positive integers: the value of the bond, and the yearly interest for that bond. The value of a bond is always a multiple of 1000$. The interest of a bond is never more than 10% of its value SAMPLE INPUT 1 10000 4 2 4000 400 3000 250


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 OUTPUT 14050

hide comments
phoemur: 2018-10-07 20:39:43

Very Nice problem...

Remember you must exploit the fact that prices are always multiples of 1000.
Simple Knapsack will TLE...

manoera262: 2018-05-17 23:05:58

Last edit: 2018-05-17 23:08:07
codiesam_007: 2018-05-10 14:49:15

One word....WOW!!

spojabhi: 2018-01-26 10:37:36

unbound knapsack+read constraints=ac.

anurag44: 2017-06-26 09:17:41

Very nyc problem..constraints to be kept in mind.!!

divyanshjr: 2017-06-23 06:13:44

Unbounded knapsack! The constraints should be read carefully. :)

steady_bunny: 2017-06-01 07:34:41

Bond will be a factor of 1000 !!!!!!

krist7599555: 2017-05-29 17:25:44

be careful
value of a bond maybe more than money you have

farhad chowdhury: 2016-04-21 03:20:08

getting tle
can anybody tell me the order of this problem.
i used both top-bottom and bottom-up

birdie: 2016-01-27 19:50:06

Last edit: 2016-01-27 19:55:09

Added by:~!(*(@*!@^&
Time limit:0.111s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:NWERC 2004