Flatten a nested dictionary into dotted keys

Given a dictionary that may contain nested dictionaries as values, produce a flattened dictionary with dot-separated keys representing the path to each non-dictionary (leaf) value. Nested empty dictionaries should not produce keys in the output. If a key is missing from a record or a value is None, keep the value as-is. Keys may already contain dots; the flattening simply joins keys with a '.' character. Implement flatten_dict(d) that accepts a dictionary d and returns a new dictionary mapping dotted paths to leaf values. Examples of behavior: - {'a': {'b': 1}} -> {'a.b': 1} - {'x': {'y': {}}} -> {} (empty nested dict produces no output) - {'k': [1,2], 'm': {'n': None}} -> {'k': [1, 2], 'm.n': None} Focus on correctness and preserving insertion order of keys encountered during a pre-order traversal.

Write a function that takes a nested dict and returns a flat dict where each key is the path of nested keys joined by dots.

- Only dict values should be recursively flattened. Other value types (lists, ints, None, etc.) are treated as leaves. - Empty nested dictionaries produce no entries. - Preserve the traversal order of keys (pre-order) when creating the output dictionary.