code: def extend_bounds(problem):
      
  
      num_vars = problem['num_vars']
      num_ff_vars = 2 ** find_smallest(num_vars)
      num_dummy_variables = num_ff_vars - num_vars
  
      bounds = list(problem['bounds'])
      names = problem['names']
      if num_dummy_variables > 0:
          bounds.extend([[0, 1] for x in range(num_dummy_variables)])
          names.extend(["dummy_" + str(var)
                        for var in range(num_dummy_variables)])
          problem['bounds'] = bounds
          problem['names'] = names
          problem['num_vars'] = num_ff_vars
  
      return problem
docs: Extends the problem bounds to the nearest power of two
  
      Arguments
      =========
      problem : dict
          The problem definition