456. Annuity Payment Scheme
Time limit per test: 0.5
Memory limit: 65536
At the peak of the Global Economic Crisis BerBank offered an unprecedented credit program. The offering was so attractive that Vitaly decided to try it. He took a loan of s
burles for m
months with the interest rate of p
Vitaly has to follow the scheme of annuity payments, meaning that he should make fixed monthly payments — x
burles per month. Obviously, at the end of the period he will pay m
burles to the bank in total.
Each of the monthly payments is divided by BerBank into two parts as follows:
- The first part ai is used to pay off the percent p of the current debt. It's clear that ai=s' · p / 100 where s'=s for the first month and equals to the remaining debt for each of the subsequent months.
- The second part bi is used to pay off the current debt. The sum of all bi over the payment period is equal to s, meaning that the borrower needs to pay off the debt completely by decreasing it from s to 0 in m months.
BerBank uses calculations with floating-point numbers, and the value of x
is uniquely determined by s
For example, if s
=50 then x
=90. For the first month a1
' · p
/ 100 = s
/ 100 = 50 and b1
= 90 - 50 = 40. For the second month a2
= (100-40) · 50 / 100 = 30, so b2
= 90 - 30 = 60 and the debt is paid off completely.
Your task is to help Vitaly and write a program that computes x
given the values of s
The single line of the input contains three integers s
(1 ≤ s
, 1 ≤ m
≤ 120, 0 ≤ p
Output the single value of monthly payment x
in burles. An absolute error of up to 10-5
100 2 50