Soccer Skills

At the company soccer tournament your boss is watching the game you are playing in. You are a good soccer player and you can make sharp passes. You look around at your team mates to see whether any of them is close enough for a reliable pass and far enough away to impress your boss.

You can reliably pass to a team mate whose distance from you is at most $b$, and your boss is impressed only when that distance is at least $a$.

The first line has an integer $N$ ($1 \le N \le 10^6$), the number of team mates on the field.

The second line has two floating point numbers $a$ and $b$ ($0 \le a, b \le 1000$). $a$ is the least distance at which your boss is impressed, and $b$ is the largest distance at which you can reliably pass.

The third line has two integers $p_x$ and $p_y$ ($-1000 \le p_x, p_y \le 1000$), your position on the playing field.

Each of the next $N$ lines has two integers $q_x$ and $q_y$ ($-1000 \le q_x, q_y \le 1000$), the position of one team mate.

If no team mate is at a distance of at least $a$ and at most $b$ from you, print one line with the word impossible.

Otherwise several team mates may qualify. Take the one with the smallest $q_x$, and if several of them remain, take the one with the smallest $q_y$. Print one line with four values separated by single spaces: the integers $q_x$ and $q_y$, the distance from you to that team mate, and the angle at which you have to shoot. The angle lies in $[-\pi, \pi)$ and is measured counter-clockwise from the positive $x$ axis. Print the distance and the angle rounded to 8 digits after the decimal point.