UMP test for an exponential mean

Let $X_1,X_2,…,X_n$ be a random sample of size $n$ ($\ge 2$) from a population having probability density function $f(x;\lambda) = \begin{cases} \frac{1}{\lambda} e^{-x/\lambda} & \text{if } x \ge 0 \ 0 & \text{otherwise,} \end{cases}$ where $\lambda > 0$ is an unknown parameter. Let $T_1 = \sum_{i=1}^{n} X_i$ and $T_2 = \left(\sum_{i=1}^{n} X_i\right)^{-1}$. For any positive integer $\nu$ and any $\alpha \in (0,1)$, let $\chi^2_{\nu;\alpha}$ denote the $(1 - \alpha)$-th quantile of the central chi-square distribution with $\nu$ degrees of freedom. Consider testing $H_0: \lambda = \lambda_0$ against $H_1: \lambda > \lambda_0$. Then which of the following tests is/are uniformly most powerful test at level $\alpha$?