Bild Union for each element

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I'm searching for an operator (replace the ?), to solve this equation:

$$ M ? \{ K, L \} = \{ M \cup K, M \cup L \} $$

M, K, L are sets.

Does something like this exist?

(Actually $\{ K, L \}$ is a power set, but I think this doesn't matter.)


To clarify my question: I'm searching for a short way to write:

$$ \{a\}, \{a, b\}, \{a, c\}, \{a, b, c\} $$

So $M = \{a\}$ and $K, L$ are wildcards for elements from $\mathcal{P}(b, c)$