CF1168E Xor Permutations

Toad Mikhail has an array of $ 2^k $ integers $ a_1, a_2, \ldots, a_{2^k} $ . Find two permutations $ p $ and $ q $ of integers $ 0, 1, \ldots, 2^k-1 $ , such that $ a_i $ is equal to $ p_i \oplus q_i $ for all possible $ i $ , or determine there are no such permutations. Here $ \oplus $ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

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