Monte
-----

You work for Applied Probability Enterprises Inc., and
have been asked by one of their customers to write a
program that answers the question:

  If N points are placed uniform randomly in the unit
  interval, what is the probability that the smallest
  distance between two of these points will be at most
  D.

Note that the end points of the unit interval itself DO
NOT count as points to which a distance can be measured.


Input
-----

For each of several test cases, a line containing just

	N D
where

    2 <= N <= 20		0 < D < 1

D has exactly 4 decimal places.  Input ends with an end
of file.


Output
------

For each test case, a line containing just

	N D P

where N and D are copied from the input and P is the
desired probability.  D has exactly 4 decimal places
and P has exactly 2 decimal places. 


Sample Input
------ -----

 8 0.0200
10 0.0200
10 0.0100
10 0.0050
15 0.0050
15 0.0020
20 0.0020


Sample Output
------ ------

8 0.0200 0.70
10 0.0200 0.86
10 0.0100 0.61
10 0.0050 0.37
15 0.0050 0.66
15 0.0020 0.35
20 0.0020 0.54


File:	   monte.txt
Author:	   Bob Walton <walton@seas.harvard.edu>
Date:	   Fri Aug 12 21:42:59 EDT 2016

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