Find $x_N$ such that $ \lim_{N \to \infty} \log\frac{x_N}{N^2} = A $ and $ \lim_{N \to \infty} \frac{1}{N} \log(1 - x_N) = B $

Question

I have for some $A,B \in \mathbb{R}$ a sequenc $x_N \in \mathbb{R}$ such that

$$ \lim_{N \to \infty} \log\frac{x_N}{N^2} = A $$ and yet

$$ \lim_{N \to \infty} \frac{1}{N} \log(1 - x_N) = B $$ What is an example of $x_N$ which satisfies both asymptotics? What is the most susprising is first we have $\frac{1}{N^2}$ decay and in the other we have $\frac{1}{N}$. There shouldn't be a sequence that satisfies both conditions