{"raw_statement":[{"iden":"statement","content":"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. \n\nVitaly 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.\n\nEach of the monthly payments is divided by BerBank into two parts as follows: \n\nFor 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. \n\nYour task is to help Vitaly and write a program that computes x given the values of s, m and p.\n\nThe single line of the input contains three integers s, m and p (1 ≤ s ≤ 106, 1 ≤ m ≤ 120, 0 ≤ p ≤ 100).\n\nOutput the single value of monthly payment x in burles. An absolute error of up to 10 - 5 is allowed.\n\n"},{"iden":"input","content":"The single line of the input contains three integers s, m and p (1 ≤ s ≤ 106, 1 ≤ m ≤ 120, 0 ≤ p ≤ 100)."},{"iden":"output","content":"Output the single value of monthly payment x in burles. An absolute error of up to 10 - 5 is allowed."},{"iden":"examples","content":"Input100 2 50Output90.00000"}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ s \\in \\mathbb{R}^+ $ be the initial loan amount (in burles).  \nLet $ m \\in \\mathbb{Z}^+ $ be the number of months.  \nLet $ p \\in \\mathbb{R} $ be the monthly interest rate (in percent).  \nLet $ x \\in \\mathbb{R}^+ $ be the fixed monthly payment.  \n\nLet $ d_0 = s $, and for $ i = 1, \\dots, m $, define the debt after $ i $ payments recursively:  \n$$\nd_i = d_{i-1} \\left(1 + \\frac{p}{100}\\right) - x\n$$\n\n**Constraints**  \n1. $ 1 \\leq s \\leq 10^6 $  \n2. $ 1 \\leq m \\leq 120 $  \n3. $ 0 \\leq p \\leq 100 $  \n\n**Objective**  \nFind $ x $ such that $ d_m = 0 $.  \n\nThat is, solve for $ x $ in:  \n$$\ns \\left(1 + \\frac{p}{100}\\right)^m = x \\sum_{k=0}^{m-1} \\left(1 + \\frac{p}{100}\\right)^k\n$$\n\nEquivalently:  \n$$\nx = s \\cdot \\frac{r (1 + r)^m}{(1 + r)^m - 1}, \\quad \\text{where } r = \\frac{p}{100}\n$$","simple_statement":"Given loan amount s, months m, and interest rate p, find the fixed monthly payment x such that after m payments, the loan is fully paid, with interest applied monthly on the remaining balance.","has_page_source":false}