#-------------------------------------------------------------------------------
#  SequenceTemplate.py
#  Two functions that return generators.
#-------------------------------------------------------------------------------

def power_remainder(n, m, r):
   """
   Returns a generator of the (infinite) sequence of positive integers that 
   are (1) exact powers of n and (2) have remainder r upon division by m.
   """
   
   



# end

def common_terms(g, h):
   """
   Returns a generator of the sequence of terms that are common to the two 
   (increasing) sequences produced by generators g and h.
   """





   # end
# end

def main():

   A = power_remainder(2, 3, 1)
   B = power_remainder(3, 5, 4)
   C = common_terms(power_remainder(2, 3, 1), power_remainder(3, 5, 4))

   print()
   for i in range(15):
      s = "  {0:<12}{1:<12}{2:<12}".format(next(A), next(B), next(C))
      print(s)
   # end
   print()

# end

#-------------------------------------------------------------------------------
if __name__=='__main__':

   main()

# end

"""
Expected output:

  1           64          64
  4           729         117649
  16          2744        262144
  25          6859        4826809
  49          13824       24137569
  64          24389       113379904
  100         39304       148035889
  121         59319       481890304
  169         85184       1073741824
  196         117649      2565726409
  256         157464      3010936384
  289         205379      6321363049
  361         262144      10779215329
  400         328509      19770609664
  484         405224      22164361129

"""