456. Annuity Payment Scheme
Time limit per test: 0.5
second(s)
Memory limit: 65536
kilobytes
input: standard
output: standard
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 percent.
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 ·
x burles to the bank in total.
Each of the monthly payments is divided by BerBank into two parts as follows:
 The first part a_{i} is used to pay off the percent p of the current debt. It's clear that a_{i}=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 b_{i} is used to pay off the current debt. The sum of all b_{i} 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 floatingpoint numbers, and the value of
x is uniquely determined by
s,
m and
p.
For example, if
s=100,
m=2,
p=50 then
x=90. For the first month
a_{1} =
s' ·
p / 100 =
s ·
p / 100 = 50 and
b_{1} = 90  50 = 40. For the second month
a_{2} = (10040) · 50 / 100 = 30, so
b_{2} = 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,
m and
p.
Input
The single line of the input contains three integers
s,
m and
p (1 ≤
s ≤ 10
^{6}, 1 ≤
m ≤ 120, 0 ≤
p ≤ 100).
Output
Output the single value of monthly payment
x in burles. An absolute error of up to 10
^{5} is allowed.
Example(s)
sample input

sample output

100 2 50

90.00000
