Beautiful name
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 M and is the lexicographically smallest among all possible names. You are provided with all the names currently used in the tribe and the number M. Your task is to determine the beautiful name or indicate that it does not exist.
Input
The first line of the input contains two integers N and M (1 ≤ N ≤ 500, 1 ≤ M ≤ 500)—representing the number of names in the tribe and the desired length of the beautiful name. Each of the following N lines contains S_i, the i-th name in the tribe. The length of each name does not exceed 500, and each name consists solely of lowercase English letters.
Output
If a suitable name exists, print it. Otherwise, print "Impossible" (without quotes).