Lecture Room Reservation System

Chungnam National University's Engineering Building 5 has $N$ lecture rooms numbered from $1$ to $N$. Students reserve a room through the reservation system before using it. To reserve a room, a student sends the room number $k$, a start time $s$, and an end time $e$ to the system.

One day, the system receives $M$ reservation requests. The requests arrive in order of start time $s$ from earliest to latest, and no two requests share the same start time. The system checks the requests in order. If a request does not overlap any reservation already accepted for the same room, the system accepts it. Otherwise, it rejects it. Two reservations where one ends at the exact time the other starts do not overlap.

Given the $M$ requests, determine whether the system accepts or rejects each one.

The first line contains integers $N$ and $M$ ($1 \le N, M \le 200\,000$).

Each of the next $M$ lines contains a room number $k_i$ ($1 \le k_i \le N$) and integers $s_i$ and $e_i$ ($1 \le s_i < e_i \le 10^9$), the start and end times of the $i$-th reservation. The reservations are given in ascending order of $s$, and no two share the same start time.

Print $M$ lines. For each request in order, print YES if the system accepts it, or NO if it rejects it.

Slow input and output can cause a time limit exceeded when reading or printing many lines.

If you use C++ with cin and cout, apply both cin.tie(NULL) and sync_with_stdio(false), and write \n instead of endl. After this, do not use C-style I/O such as scanf, printf, puts, getchar, or putchar.

If you use Java, you can use BufferedReader and BufferedWriter instead of Scanner and System.out.println. Call BufferedWriter.flush only once, at the end.

If you use Python, you can use sys.stdin.readline instead of input. It keeps the trailing newline, so call .rstrip() when you store a string.