410343: GYM104011 C Clean Up!

Once Charlie decided to start a new life by deleting all files in his Downloads directory. It's easy to do that using bash shell! It has two useful features: the "rm" command, which removes all files given as arguments, and patterns, which are replaced with the list of files matching them before executing the command.

Charlie ran "rm *", but received an "Argument list too long" response. Unfortunately, after bash replaced "*" with the names of all files in the Downloads directory, it failed to run the command because it had too many arguments.

After some experiments, Charlie realized he can execute "rm abc*" to delete all files with names starting with "abc" if there are at most $$$k$$$ such files. If more than $$$k$$$ files match this pattern, none of them will be deleted. Of course, he can replace "abc" with any string.

Help Charlie to find the smallest number of "rm" commands needed to delete all files. Assume that he can only use the "rm" command as "rm <prefix>*", where <prefix> consists of lowercase English letters (and can be empty).

The first line contains two integers $$$n$$$ and $$$k$$$ — the number of files to delete, and the maximum number of files that can be deleted by one "rm" command ($$$1 \le n, k \le 3 \cdot 10^5$$$).

Each of the next $$$n$$$ lines contains a single string, denoting a file name. All file names are distinct, non-empty, and consist of lowercase English letters. The total length of all file names doesn't exceed $$$3 \cdot 10^5$$$.

Print a single integer — the smallest number of "rm" commands needed to delete all files.

4 2
a
abc
abd
b

2

4 2
d
c
ab
a

2

5 3
please
remove
all
these
files

3

In the first example test, Charlie can execute "rm ab*" to delete files "abc" and "abd", and then execute "rm *" to delete files "a" and "b". Note that he can't just run "rm *" immediately, because initially all four files match an empty prefix.