Hotel Booking System

You are given a hotel with M rooms, numbered from 0 to M-1. Initially, all rooms are available. The hotel booking manager processes a series of commands to book a range of rooms or check the availability of a single room.

The input begins with two integers, M and a dummy parameter R (which can be ignored), followed by an integer N denoting the number of commands. Each of the next N lines contains a command in one of the following formats:

• BOOK x y — book all rooms from x to y (inclusive).
• CHECK z — check if room z is booked. If it is, output \(\text{booked}\); otherwise, output \(\text{available}\).

For each CHECK command, print the result on a separate line.

Note: Room indexing is 0-based. The dummy parameter R provided in the first line does not affect the simulation.

The mathematical notation for the check result can be represented as follows in \(\LaTeX\):

[ \text{result} = \begin{cases} \text{booked} & \text{if the room is already booked} \ \text{available} & \text{otherwise} \end{cases} ]

inputFormat

The input is read from stdin and has the following structure:

1. The first line contains two integers M and R (where R is a dummy parameter).
2. The second line contains an integer N representing the number of commands.
3. Each of the following N lines contains one command in one of these formats:
• BOOK x y
• CHECK z

All numbers are integers, and room indices are zero-indexed.

outputFormat

For each CHECK command, output the result on a new line to stdout. The output should be:

• booked if the checked room has been booked by any previous BOOK command.
• available if the room is still free.

For example, the output for a series of CHECK commands might be:

booked
available
booked

## sample

10 5
5
BOOK 2 5
CHECK 4
CHECK 6
BOOK 0 1
CHECK 1

booked
available
booked

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