Case 1:
  N = 3
  k = 4
  g = 110

Case 2:
  N = 4
  k = 13
  g = 1011

Case 3:
  N = 10
  k = 1023
  g = 1000000000

Case 4:
  N = 12
  k = 1000
  g = 001000011100