Once Charlie decided to start a new life by deleting all files in his Downloads directory. It's easy to do that using \t{bash} shell! It has two useful features: the ``\texttt{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 ``\texttt{rm *}'', but received an ``\texttt{Argument list too long}'' response. Unfortunately, after \t{bash} replaced ``\texttt{*}'' 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 ``\texttt{rm abc*}'' to delete all files with names starting with ``\texttt{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 ``\texttt{abc}'' with any string. Help Charlie to find the smallest number of ``\texttt{rm}'' commands needed to delete all files. Assume that he can only use the ``\texttt{rm}'' command as ``\texttt{rm <prefix>*}'', where \texttt{<prefix>} consists of lowercase English letters (and can be empty). \InputFile 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 ``\texttt{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 $3 \cdot 10^5$. \OutputFile Print a single integer~--- the smallest number of ``\texttt{rm}'' commands needed to delete all files. \Note In the first example test, Charlie can execute ``\texttt{rm ab*}'' to delete files ``\texttt{abc}'' and ``\texttt{abd}'', and then execute ``\texttt{rm~*}'' to delete files ``\texttt{a}'' and ``\texttt{b}''. Note that he can't just run ``\texttt{rm *}'' immediately, because initially all four files match an empty prefix.