CF48F Snow sellers

The New Year celebrations in Berland last $ n $ days. Only this year the winter is snowless, that’s why the winter celebrations’ organizers should buy artificial snow. There are $ m $ snow selling companies in Berland. Every day the $ i $ -th company produces $ w_{i} $ cubic meters of snow. Next day the snow thaws and the company has to produce $ w_{i} $ cubic meters of snow again. During the celebration new year discounts are on, that’s why the snow cost decreases every day. It is known that on the first day the total cost of all the snow produced by the $ i $ -th company is equal to $ c_{i} $ bourles. Every day this total cost decreases by $ a_{i} $ bourles, i.e. on the second day it is equal to $ c_{i}-a_{i} $ ,and on the third day — to $ c_{i}-2a_{i} $ , and so on. It is known that for one company the cost of the snow produced by it does not get negative or equal to zero. You have to organize the snow purchase so as to buy every day exactly $ W $ snow cubic meters. At that it is not necessary to buy from any company all the snow produced by it. If you buy $ n_{i} $ cubic meters of snow ( $ 0

The first line contains integers $ n $ , $ m $ and $ W $ ( $ 1

Print a single number — the answer to the given problem. Print the answer in the format with the decimal point (even if the answer is integer, it must contain the decimal point), without "e" and without leading zeroes. The answer should differ with the right one by no more than $ 10^{-9} $ .