Given two integers n and start, return a permutation p of integers from $0$ to $2^n - 1$ such that:

• p[0] = start

• p[i] and p[i + 1] differ by exactly one bit in their binary representation for all $0 \leq i < 2^n - 1$.

• The first element p[0] and the last element p[2^n - 1] also differ by exactly one bit in their binary representation.

Constraints:

• $1 \leq$ n $\leq 16$

• $0 \leq$ start $< 2^n$

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