SGU 456 Annuity Payment Scheme

D - Annuity Payment Scheme

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

Submit Status Practice SGU 456

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 s, m and p. 

For example, if s=100, m=2, p=50 then x=90. For the first month a₁ = s' · p / 100 = s · p / 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, 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.

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

/*************************************************************************
    > File Name: code/2015summer/#5/D.cpp
    > Author: 111qqz
    > Email: rkz2013@126.com 
    > Created Time: 2015年07月30日 星期四 13时17分26秒
 ************************************************************************/

#include<iostream>
#include<iomanip>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<string>
#include<map>
#include<set>
#include<queue>
#include<vector>
#include<stack>
#define y0 abc111qqz
#define y1 hust111qqz
#define yn hez111qqz
#define j1 cute111qqz
#define tm crazy111qqz
#define lr dying111qqz
using namespace std;
#define REP(i, n) for (int i=0;i<int(n);++i)  
typedef long long LL;
typedef unsigned long long ULL;
const int inf = 0x7fffffff;
int s,m,p;
double ans;

double cal(double x,int n)
{
    double res = 1.0;
    for ( int i = 1 ; i <= n ; i++ )
    {
    res = res * x;
    }
  //  cout<<"res:"<<res<<endl;
    return res;
}
int main()
{
    cin>>s>>m>>p;
    double sum = 0;
    double per = p*1.0/100+1;
    for ( int i = 1 ; i <= m;  i++ )
    {
    sum=sum+1.0/cal(per,i);
//    cout<<"sum:"<<sum<<endl;
    }
 //   cout<<sum<<endl;
    cout<<fixed<<setprecision(5)<<s*1.0/sum<<endl;
  
    return 0;
}