Description
People who study epidemiology use models to analyze the spread of disease. In this problem, we use a simple model.
When a person has a disease, they infect exactly R other people but only on the very next day. No person is in fected more than once.
We want to determine when a total of more than P peoplehave had the disease.
(This problem was designed before the current coronavirus outbreak, and we acknowledge the distress currently being experienced by many people world wide because
of this and other diseases.
We hope that including this problem at this time highlights the important roles that computer science and mathematics play in solving real-world problems.)
Input
There are three lines of input. Each line contains one positive integer.
The first line contains the valueof P.
The second line contains N,the number of people who have the diseaseon Day 0.
The third line contains the value of R. Assume that P ≤ 107 and N ≤ P and R ≤ 10.
Output
Output the number of the first day on which the total number of people who have had the disease is greater than P.
HINT
SampleInput1
750
1
5
OutputforSampleInput1
4
Explanation of Output for Sample Input 1
The 1 person on Day 0 with the disease infects 5 people on Day 1. On Day 2,
exactly 25 people are infected. On Day 3, exactly 125 people are infected.
A total of 1 + 5 + 25 + 125 + 625 = 781 people have had the disease by the end of Day 4 and 781 > 750.
SampleInput2
10
2
1
OutputforSampleInput2
5
Explanation of Output for Sample Input 2
Thereare 2 peopleonDay0withthedisease.
Oneachotherday,exactly 2 peopleareinfected. By the end of Day 4,
a total of exactly 10 people have had the disease and by the end of Day 5, more than 10 people have had the disease.