Non-existence of certain test size

Let $X_1, X_2, X_3, X_4$ be a random sample from a distribution with the probability mass function $$f(x)=\begin{cases} \theta^x(1-\theta)^{1-x}, & x=0, 1 \ 0, & \text{otherwise,} \end{cases}$$ where $\theta\in(0, 1)$ is unknown. Let $0 < \alpha \le 1$. To test the hypothesis $H_0: \theta=\frac{1}{2}$ against $H_1: \theta > \frac{1}{2}$, consider the size $\alpha$ test that rejects $H_0$ if and only if $\sum_{i=1}^4 X_i \ge k_\alpha$, for some $k_\alpha \in \{0, 1, 2, 3, 4\}$. Then for which one of the following values of $\alpha$, the size $\alpha$ test does NOT exist?