Almost Prefix-Free Codes

In coding theory, prefix-free codes are used often: sets of words such that no word is a prefix of another. (A word $\alpha$ is a prefix of a word $\beta$ if $\alpha$ can be obtained from $\beta$ by deleting zero or more characters from its end. For example, the words <<>>, <>, <>, and <> are prefixes of the word <>.) For instance, the set of words <>, <>, and <> is a prefix-free code, while the set <>, <>, <> is not, because <> is a prefix of <>.

Professor Deshifro works at the laboratory for the study of useless information and is researching his new invention: almost prefix-free codes. A set of words is called an almost prefix-free code of level $k$ if the longest common prefix of any two words in the set has length at most $k$. For example, the set <>, <>, <> is an almost prefix-free code of level 2, while the set <>, <>, <> is not, because the longest common prefix of <> and <> has length 3.

The next task Professor Deshifro has assigned to his assistants is the following: given a set of words and a number $k$, choose from the given words a maximum set that is an almost prefix-free code of level $k$. As the most junior assistant, you have been tasked with writing the corresponding program.

The first line of the input file contains two integers $n$ and $k$: the number of words in the given set and the level of the almost prefix-free code to be built ($1 \le n \le 100\,000$, $0 \le k \le 200$). The next $n$ lines contain one word each. The words consist of lowercase Latin letters. The length of each word is from 1 to 200 characters. The total length of all words does not exceed $10^6$. All words are distinct.

On the first line of the output file, print a single number $m$: the maximum number of words that can be chosen from the given set so that they form an almost prefix-free code of level $k$. The next $m$ lines must contain the chosen words.