[Python] how to "zip" two nested dictionaries

I have a nested dict with different levels of nesting

dict1 = {
'A': {'a': 1},
'B': 2,
'C': {'c': 3},
'D': {'d': {'dd': 4}}
}


I want to perform (for instance) key-wise multiplication. With flat dict this is straightforward:

{k: v * 2 for k, v in dict.items()}


How can I do the same in the above dict?

A follow-up question is processing a pair of nested dicts with partial key overlap.

dict2 = {
'A': {'a': 1},
'D': {'d': {'dd': 4}}
}


A key-wise addition of flat dicts is straightforward:

{k: dict1[k] + dict2[k] for k, v in dict2.items()}


How can I do the same with nested dicts?

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