Falling Cards

Standing a playing card on its edge is hard, but someone patiently stood $N$ cards on a desk, each resting on its shorter edge. Seen from above, each card is a line segment on the desk; card $i$ runs from $(x_i, y_i)$ to $(v_i, w_i)$. Every card has the same height $H$, and no two segments intersect.

The first card is pushed and falls flat. As a card falls flat, its rectangular face covers a region of the desk: the base segment stays fixed, and the card covers the rectangle obtained by extending that segment a distance $H$ in the falling direction (perpendicular to the segment). Any still-standing card whose segment is touched by this rectangle also falls.

The first card falls in the direction obtained by rotating the vector $(x_1, y_1) \to (v_1, w_1)$ by $90^\circ$ counter-clockwise.

When a falling card $A$ touches a standing card $B$, card $B$ falls in whichever of the two directions perpendicular to its own segment makes the ray along its falling direction avoid crossing the line that contains card $A$'s segment; that is, $B$ topples away from the card that pushed it.

The input never contains:

1. a card that falls exactly perpendicular to the card that pushed it, or
2. a falling card that touches more than one still-standing card.

Determine which cards fall and which remain standing.

The first line contains the number of cards $N$ and the card height $H$ ($1 \le N \le 100$, $H > 0$; $H$ is a real number). Each of the next $N$ lines contains four real numbers $x_i\ y_i\ v_i\ w_i$, separated by spaces — the endpoint coordinates of card $i$'s segment.

Print the numbers of the cards that fall, in increasing order, separated by spaces.