Beautiful name#3363
In the Ararara tribe, as part of the initiation into adulthood, each individual must select a unique name that does not include any other name already in use within the tribe. Zerator, who is preparing for this ritual, desires to choose a beautiful name. He defines a name as beautiful if it has a length of and is the lexicographically smallest among all possible names. You are provided with all the names currently used in the tribe and the number . Your task is to determine the beautiful name or indicate that it does not exist.
The first line of the input contains two integers and (1 \leq N \leq 500, 1 \leq M \leq 500) — representing the number of names in the tribe and the desired length of the beautiful name. Each of the following lines contains S_i, the -th name in the tribe. The length of each name does not exceed , and each name consists solely of lowercase English letters.
If a suitable name exists, print it. Otherwise, print "Impossible".
Example 1