10. Let the set $M=\{1,2, \cdots, 2023\}$, for a subset $A=\left\{a_{1}, \cdots, a_{k}\right\}$ of $M$, let it correspond to a number $\alpha=(-1)^{a_{1}+\cdots+a_{k}}$ (the empty set $\varnothing$ corresponds to the number $\alpha=(-1)^{0}=1$). For all subsets $A$ of $M$, find the sum of the numbers they correspond to $\sum_{A \subseteq M} \alpha$.