Statistical Inference — sufficiency of partitioned Poisson statistics

Let $x_1,x_2,…,x_n$ be a random sample from Poisson distribution with mean $\lambda>0$. If $T_1=\sum_{i=1}^n x_i$ and $T_2=(x_1,\sum_{i=2}^n x_i)$ are the statistics, then which of these statistics is/are sufficient for $\lambda$?