Glacier Travel

Glaciers are vast rivers of slowly-flowing ice, fraught with crevasses
which hide under thin layers of snow and wait for unsuspecting walkers to step into
and fall in. To reduce the danger, hikers usually go in teams tied together
with a thick rope to reduce the consequences of a fall-if one person
falls in, the other person may yet hold them from a safe distance.


Today, you are roped up to cross a glacier with your partner. Your plan is to
follow the exact same route, at the same speed, the first starting earlier and
the second beginning to trace steps once you are exactly  metres apart. Were
you to follow a completely straight path, you would thus then remain exactly 
metres apart at all time.

figure[!h]
sample2.pdf
An illustration of the path taken in the 2nd sample case, taken from above.
         This could also be a particularly festive diagram of someone falling into a crevasse.
figure

However, the twisting nature of the course as you avoid obstacles means that
you may not always remain exactly  metres apart. What is the closest that you
shall actually come while both of you are walking on the path?

Input
	itemize
    One line containing a real number: the separation distance along the
          path in metres,  ().
    One line containing the number of points in the path,
           ().
     further lines, the th of which contains a pair of integers
          giving the th coordinate on the track  ()
          in metres from the origin.
	itemize

  Every pair of adjacent points on the track are distinct from one another,
  although the track may cross over or repeat itself. The track is guaranteed
  to have a length of at least .

Output
  Output the minimum distance between the two walkers at any point on the route,
  ignoring any time after the first walker has finished, or before the second
  walker has started.

  The output must be accurate to an absolute or relative error of at most
  .
