Let's Go to the Movies

Input

Your program will be tested on one or more test cases. The first line of each test case contains two positive integers $S$ and $F$ , where $S$ is the price of a single ticket and $F$ is the price of a family ticket. The following lines of the test case are either the name of a person going alone or are of the form:

N $_{1}$ _1 N $_{2}$ _2 N $_{3}$ _3 $\dots$ N $_{k}$ _k

where $N_{1}$ N_1 is the name of a parent, and $N_{2}, \dots, N_{k}$ N_2, \ldots, N_k are his or her children. Names are composed only of lowercase letters and are no longer than $1000$ characters. No parent will take more than $1000$ children to the movies. Names are unique, and a particular person's name can appear at most twice: once as a parent, and once as a child. There will be at least one person and at most $100000$ people in any test case.

The end of a test case is indicated by the beginning of the next test case (a line with two integers). The end of the last test case is indicated by a line with two zeros.

Output

For each test case, output the result in the following format:

$k$ . $N S$ $N F$ $T$

where $k$ is the test case number (starting from $1$ ), $N S$ is the number of single tickets, $N F$ is the number of family tickets, and $T$ is the total ticket price.

Examples

Example 1

Loading