SGU 456 Annuity Payment Scheme-白红宇

SGU 456 Annuity Payment Scheme

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发布时间：2019-06-07

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D - Annuity Payment Scheme

Time Limit:500MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u

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Description

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

m and

For example, if

s=100,

m=2,

p=50 then

x=90. For the first month

₁ =

s' ·

p / 100 =

s ·

p / 100 = 50 and

₁ = 90 - 50 = 40. For the second month

₂ = (100-40) · 50 / 100 = 30, so

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

m and

Input

The single line of the input contains three integers

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.

Sample Input

sample input

sample output

100 2 50

90.00000

水题,推个公式出来,注意精度...一遍A

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