require "rational"
class Rational
  def expand(b=10,w=nil)
    raise ArgumentError, "#{b} > 36" if b > 36
    n, d, v = @numerator, @denominator, self < 0 ? "-" : ""
    return v<<itos(n,b) if d == 1 or d == n
    v << itos(n.div(d), b) << "."
    quo, rem, n = [], [], n.modulo(d)
    if w
      w.times do n *= b; q, n = n.divmod(d); quo<<q end
      v << quo.map{|n| itos(n,b)}.join
    else
      until i = rem.rindex(n) do rem<<n; n *= b; q, n = n.divmod(d); quo<<q end
      v<<"#{quo[0...i].map{|n| itos(n,b)}}(#{quo[i..-1].map{|n| itos(n,b)}})"
    end
  end

  DIGIT36 = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"

  def itos(n,b)
    return "0" if n.zero?
    v = ""
    until n == 0 do r,q = n.divmod(b); v<<DIGIT36[q.to_i]; n = r end
    v.reverse
  end
end

class Float
  def to_rational
    s,e,m=/(.{1})(.{11})(.{52})/.match([self].pack("G").unpack("B*").shift)[1,3]
    (-1)**s.to_i * Rational("1#{m}".to_i(2),2**(1075-e.to_i(2)))
  end
  def expand(b=10,w=nil) to_rational.expand(b,w) end
end
class Integer
  def expand(b=10) Rational(self,1).expand(b) end
end