Determine all possible positive integer(s) P such that:

2¹⁹⁹⁴ + 2¹⁹⁹⁸ + 2¹⁹⁹⁹ + 2²⁰⁰⁰ + 2²⁰⁰² + 2^P

is a perfect square.

From the statement of the problem,
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