\textit{Who’s afraid of the big bad wolf, Big bad wolf, big bad wolf? Who’s afraid of the big bad wolf? Tra-la-la-la-la!} \includegraphics{https://static.e-olymp.com/content/b9/b9f175a242145a3eb1ab434bad3501062c8c4f84.jpg} All of you well know the fairy tale about three little pigs: brothers Nif-Nif, Nuf-Nuf and Naf-Naf. Nif-nif built for himself a house of straw, Nuf-Nuf built a house of sticks, and Naf-Naf made his house of bricks, firm and strong as a stronghold. When the Wolf came in order to catch and to eat little pigs, each of them ran inside his house and shut the door. The Wolf came to the house of straw, took a deep breath and started to blow. Bit by bit, he blew off the roof, the straw walls and window frames. Very little time was necessary to him in order to destroy this house and to eat Nif-Nif. Rather more time was spent in order to blow off the house of sticks and to eat Nuf-Nuf. But the house of bricks was found as strong as the Wolf’s lifetime was not enough in order to destroy it… After that a long time passed. The population of little pigs grew up to \textbf{N} individuals. Each of them built for himself a house of some strength. But during this period of time the numbers of wolves also increased. Now there are \textbf{K} wolves, which are very hungry and want to eat all little pigs. For that it is necessary to destroy their houses. Wolves taught bitter experience of their ancestor have decided to divide their self by some packs, so each pack simultaneously with others will start to attack certain little pig’s house. After distributing wolves can not pass from one house to other. It is known, that one wolf can blow off the house of strength \textbf{P} during \textbf{P} hours, two wolves done it during \textbf{P/2} hours, etc. For destroying the house of strength \textbf{P} by \textbf{K} wolves it is necessary \textbf{P/K} hours. Help wolves to determine in how much time they can catch and eat all little pigs. \InputFile Input file consists of several data sets. In the first line of each set two integers \textbf{K} and \textbf{N} (the numbers of wolves and little pigs correspondingly) are given. (\textbf{1} ≤ \textbf{K} ≤ \textbf{10^8}, \textbf{1} ≤ \textbf{N} ≤ \textbf{10^5}). The second line contains \textbf{N} integers \textbf{P_1}, \textbf{P_2}, …, \textbf{P_N}, separated by single space, where \textbf{P_i} (\textbf{1} ≤ \textbf{P_i} ≤ \textbf{10^9}) --- the strength of the house of \textbf{i}-th little pig. The pair of values \textbf{K=N=0} indicates end of input file. \OutputFile In the output file write one real number accurate to at least \textbf{6} digits after decimal point --- minimal time necessary to wolves in order to destroy houses of all little pigs. In the case of impossibility of destroying all houses, write the word "\textbf{Impossible}". The answer for each data set must be written in a separate line.