input: Write a function to generate an inverted dictionary from the given dictionary. The function should return a new dictionary where the keys and values are swapped, and if there are multiple keys with the same value, those keys should be grouped together in a list under the new value. If the input dictionary is empty, the function should return an empty dictionary.
  
  def invert_dictionary(d):
      inverted_d = {}
  
      for key, value in d.items():
          if value not in inverted_d:
              inverted_d[value] = []
          inverted_d[value].append(key)
  
      return inverted_d
  
  assert invert_dictionary({'a': 1, 'b': 2, 'c': 1}) == {1: ['a', 'c'], 2: ['b']}
  assert invert_dictionary({'x': 'apple', 'y': 'banana', 'z': 'banana'}) == {'apple': ['x'], 'banana': ['y', 'z']}
  assert invert_dictionary({}) == {}
output: def invert_dictionary(d):
      inverted_d = {}
  
      for key, value in d.items():
          if value not in inverted_d:
              inverted_d[value] = []
          inverted_d[value].append(key)
  
      return inverted_d