Czech ACM Student Chapter

Czech Technical University in Prague

Charles University in Prague

Technical University of Ostrava

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Slovak University of Technology

Pavol Jozef Safarik University in Koˇice

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University of Zilina

Masaryk University

Matej Bel University in Bansk´ Bystrica

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University of West Bohemia

CTU Open Contest 2012

Mosquito Multiplication

mosquito.c, mosquito.cpp, Mosquito.java

Have you ever wondered why there are so many mosquitos in wet environments? One of the

reasons is that adult female mosquitos can lay as many as hundreds of eggs. Even if most of them

do not (fortunately!) survive, it is said that a single pair of mosquitos can generate a population

of thousands in just a couple of weeks. Let us have a closer look at these numbers.

The mosquito life cycle includes four stages: egg, larva, pupa, and adult. For simplicity, we will

make several assumptions that are not quite true in the nature: The egg stage lasts less than

one day, and all the other stages are one week long. Each mosquito lives as a larva for the first

week, the second week "hibernates" in the form of a pupa, and finally, the third week lives as

an adult mosquito. At the end of its three-week life, each mosquito lays eggs and dies.

To simplify things even further, we will assume that the transformation from one life stage into

another always happens on Sunday. Each Sunday, the following things happen:

· An adult mosquito lays E eggs and dies. Within a day, one larva hatches from each egg.

· Some of the larvae hatched from egg the last Sunday were not strong enough and died or

got eaten. Only every R-th larva will transform into a pupa on Sunday.

· An adult mosquito emerges from every S-th pupa, all other pupae dry.

For example, if there are 5 pupae and every 3-rd of them survives, there will be 1 mosquito left.

Out of 6 pupae, two adult mosquitos emerge.

In the first week, there are M mosquitos, P pupae and L larvae. Calculate how many mosquitos

will there be after N Sunday transformations. Of course, we are counting only living adult

mosquitos, not the dry dead bodies.

Input Specification

The input consists of several instances, each instance per one line. Each line contains seven

integers M , P , L, E, R, S, N separated by space. M , P and L are the numbers of mosquitos,

pupae, and larvae, respectively, in the first week. You may assume that 0 ≤ M, P, L ≤ 100 000,

0 ≤ E ≤ 100, 1 ≤ R, S ≤ 10, and 1 ≤ N ≤ 1000. E is the number of eggs laid by one mosquito,

R and S specify the survival rates of larvae and pupae, and N is the number of weeks.

Output Specification

For each input instance, output a single line containing an integer number C , giving the count

of mosquitos after the N -th Sunday.

You may assume that the number of mosquitos during each of the first N weeks will not exceed

1 000 000.

Sample Input

10 20 40

4 2 2 10

144 55 8

0194

10 10 10

2326

10 20 40

86 9 9 999

Output for Sample Input

10

0

1

10