This is a sequel to part #1, with the same setup, but a different goal.

A folder system on a computer might look something like the picture below:

In this challenge, folder systems will be represented by dictionaries where the keys are folders X and the value at X is the list of subfolders of X.

For example, the picture above becomes the dictionary:

{
  "A": ["B", "C", "D"],
  "B": ["E", "F"],
  "D": ["G", "H"],
  "G": ["I", "J"],
  "H": ["K"]
}

The inputs for this challenge will be:

• A dictionary representing a folder system.
• Two folders X and Y.

Write a function that finds the "smallest" folder containing both X and Y (in the illustration, this is the lowest folder for which you can travel down to both X and Y; or, if you view the system as a "family tree", this is the last common ancestor).

Examples

last_ancestor({
  "A": ["B", "C", "D"],
  "B": ["E", "F"],
  "D": ["G", "H"],
  "G": ["I", "J"],
  "H": ["K"]
}, "B", "C") ➞ "A"

last_ancestor({
  "A": ["B", "C", "D"],
  "B": ["E", "F"],
  "D": ["G", "H"],
  "G": ["I", "J"],
  "H": ["K"]
}, "I", "J") ➞ "G"

last_ancestor({
  "A": ["B", "C", "D"],
  "B": ["E", "F"],
  "D": ["G", "H"],
  "G": ["I", "J"],
  "H": ["K"]
}, "I", "K") ➞ "D"

last_ancestor({
  "A": ["B", "C", "D"],
  "B": ["E", "F"],
  "D": ["G", "H"],
  "G": ["I", "J"],
  "H": ["K"]
}, "D", "I") ➞ "D"

last_ancestor({
  "A": ["B", "C", "D"],
  "B": ["E", "F"],
  "D": ["G", "H"],
  "G": ["I", "J"],
  "H": ["K"]
}, "G", "G") ➞ "G"

Notes

• All the examples above use the folder system in the illustration, but the tests will use other folder systems as well.
• For the purposes of this challenge, any folder is inside itself, as in the last two examples.