Wolves#238
Once upon a time, the wolves failed to blow down a house of bricks...
Everyone knows the story of the three little pigs: Nif-Nif, Nuf-Nuf, and Naf-Naf. Nif-Nif built a house of straw, Nuf-Nuf a house of sticks, and Naf-Naf built a solid house of bricks, strong like a fortress. When the Wolf came to eat the pigs, each hid inside his own house. The Wolf approached the straw house, took a deep breath, and blew at the house, bit by bit blowing away the roof, the straw walls, the windows, etc. It took him very little time to destroy the house and eat Nif-Nif. Blowing down the house of sticks and eating Nuf-Nuf took a bit longer. But the brick house turned out so strong that the Wolf could not destroy it in his entire life…
Many years have passed since then. During this time, the pig population grew to individuals. Each built a house of a certain strength. Yet the number of wolves also increased. Now there are hungry wolves who want to eat all the pigs. To do so, they must destroy their houses. Taught by the experience of their ancestor, the wolves decided to split into several packs, each of which will attack a separate house simultaneously. Afterwards, wolves cannot move from one house to another. It is known that one wolf can destroy a house of strength in hours, two wolves in hours, etc. wolves can destroy a house of strength in hours.
Help the wolves determine how quickly they can catch and eat all the little pigs.
The input consists of several datasets. The first line of each dataset contains two integers and (1 \leq K \leq 10^8, 1 \leq N \leq 10^5) — the number of wolves and pigs, respectively. The second line contains integers P_1, P_2, \ldots, P_N (1 \leq P_i \leq 10^9) — the strengths of the pig houses. The pair K = 0, N = 0 indicates the end of the file.
For each dataset, print a real number — the minimal time required for the wolves to destroy all the houses, accurate to at least decimal places. If it is impossible to destroy all houses, print Impossible. The answer to each dataset should be printed on a separate line.
Example 1