Critical region of the most powerful test for a Laplace scale

Let $X_1,…,X_n$ be a random sample from a population with the probability density function $f(x)=\dfrac1{2\theta}e^{-|x|/\theta}$, $x\in\mathbb R$, $\theta>0$. For a suitable constant $K$, the critical region of the most powerful test for testing $H_0:\theta=1$ against $H_1:\theta=2$ is of the form