Rejection region of shifted exponential the form $ \{y_1\leq k_1\} \cup \{y_2\geq k_2\}$

Question

I need to show that the shifted exponential $f(x) = e^{-x-\beta}$ in the likelihood ratio test has the rejected region of the form $ \{y_1\leq k_1\} \cup \{y_2\geq k_2\}$ which testing $$H_0: \beta=0, H_1: \beta \neq 0$$I found out that the rejection region is $\lambda(x) : e^{-nx(1)} \leq k$ is the rejection region where x(1) is the first order statistics, but I have some trouble showing that the rejection region can be two parts. It makes sense as it is a two sided test but how to show this?