# Aperiodic Binary Strings Redux

A binary string is a string whose characters are only 0s and/or 1s. For example, $$0101, 11111, 110001$$ are binary strings.

A string $$s$$ is periodic if there exists another string $$t$$ whose length is less than $$s$$ such that concatenating several copies of $$t$$ produces $$s$$. For example, $$0101$$ is periodic ($$t = 01$$), and $$1111$$ is periodic ($$t = 11$$ or $$t = 1$$), but $$10101$$ is not periodic. A string is aperiodic if it is not periodic.

This problem asks about the number of aperiodic binary strings of length $$23$$. For this problem, compute the number of aperiodic binary strings of length $$(23!)^{23}$$ (that is, 23 factorial raised to the 23th power). Enter your answer modulo $$10^9 + 7 = 1000000007$$.

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