<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def getUnionLocations(encoder, x, y, r, step=1):
 """ Return a union of location encodings that correspond to the union of all locations within the specified circle. """

  output = np.zeros(encoder.getWidth(), dtype=defaultDtype)
  locations = set()
  for dx in range(-r, r+1, step):
    for dy in range(-r, r+1, step):
      if dx*dx + dy*dy <= r*r:
        e = encodeLocation(encoder, x+dx, y+dy, output)
        locations = locations.union(set(e))

  return locations