# We'll take this way too far

Logic Level 3

$2^0 \, \square \, 2^1 \, \square \, 2^2 \, \square \, \ldots \, \square \, 2^{1337} = A$

There are $$2^{1337}$$ ways in which we can fill the squares with $$+, -$$. Let $$B$$ denote the number of positive integer value of $$A$$ such that there exist a solution for the equation above. Find the value of $$\log_2 B$$.

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