Cyclic Marathon

A cyclic marathon takes place on a circular track of length $L$. One point on the track is the start and finish line. $N$ runners stand on the track at distances $D_i$ measured clockwise from that point and receive start numbers $1$ through $N$, starting with the runner closest to the line.

After the start signal, each runner moves clockwise at speed $S_i$. If a runner catches the runner directly ahead, the caught runner is eliminated.

The race continues until no further eliminations are possible. Every runner still on the track is a winner. Write a program that prints the elimination order.

The first line contains positive integers $N$ and $L$ ($N \leq 500\,000$, $L < 5\,000\,000$).

Each of the next $N$ lines describes one runner: starting position $D_i$ and speed $S_i$. The positions satisfy $0 \leq D_1 < D_2 < \cdots < D_N < L$, and each speed is a real number with two decimal places, $0 < S_i \leq 5$. Distances are in meters and speeds are in meters per second.

Print one line per eliminated runner with that runner's start number. Each of these lines ends with a single trailing space.

The last line must be Winner(s): followed by one space and the start numbers of all winners in increasing order, separated by single spaces.