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 floating-point 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 = (100-40) · 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.

The single line of the input contains three integers s, m and p (1 ≤ s ≤ 106, 1 ≤ m ≤ 120, 0 ≤ p ≤ 100).

Output the single value of monthly payment x in burles. An absolute error of up to 10-5 is allowed.

sample input
sample output
100 2 50