Drop by When You are Near the Ring
---- -- ---- --- --- ---- --- ----

Oliver lives on a ring, a rather large spinning circle
of metal in space.  He and his fellow Dogplovians get
around in one-time-spaceships, which are discarded
after a single use.  Typically, to get home Oliver aims
his current ship more or less at the ring, fires the
motor till its empty, then waits till he is closest to
the ring, hops in his personal spacepod, and motors
straight home in it.

Oliver has lost his computer programs and desperately
needs you to write him one that will calculate when
he is closest to his ring.  In Dogplovian coordinates,
the ring is in the xy plain centered on the origin.  The
input is the point where Oliver fired his motor and the
velocity achieved (instantaneously for computational
purposes).  For convenience assume the motor is fired
at time 0.

Note that distance to the ring is measured from the
spaceship to the nearest point on the ring, as once
Oliver gets to the ring he takes the `circle train' to
his domicile.  Note also that all distances are in
dogbounds, and times in dogbarks, but you do not really
need to use this knowledge.

Ah, and we almost forgot to mention.  Luckily for you,
Oliver lives in two dimensional space, and not three
dimensional space.


Input
-----

For each case, a single line containing the 5 numbers

	r x y vx vy

where r is the radius of the ring, (x,y) the point where
the motor is fired at time 0, and (vx,vy) the velocity
achieved at time 0.  The velocity is constant after time
0.

An end of file terminates the input.


Output
------

For each case, a single line containing the 2 numbers

	t d

where t is the time Oliver's spaceship is closest to the
ring and d is the distance between the spaceship and the
ring at that time.  Both numbers must be printed with
exactly 3 decimal places.

The input will be such that t > 0 is always true; i.e.,
the spaceship will never be headed away from the ring.


Example Input
------- -----

1.0 -1.00 2.00 1 0
1.0 0 2 0.5 -0.5
10.0 1 1 1 1
10.0 1 1 -0.1 -0.1

Example Output
------- ------

1.000 1.000
2.000 0.414
6.071 0.000
80.711 0.000


File:	   nearring.txt
Author:	   Bob Walton <walton@deas.harvard.edu>
Date:	   Thu Oct 21 07:23:18 EDT 2004

The authors have placed this file in the public domain;
they make no warranty and accept no liability for this
file.

RCS Info (may not be true date or author):

    $Author: walton $
    $Date: 2004/10/21 11:24:04 $
    $RCSfile: nearring2d.txt,v $
    $Revision: 1.5 $