Let \omega=e^{\frac{2 \pi i}{2017}} and \zeta=e^{\frac{2 \pi i}{2019}}. Let S=\{(a, b) \in \mathbb{Z} \mid 0 \leq a \leq 2016,0 \leq b \leq 2018,(a, b) \neq(0,0)\}. Compute \prod_{(a, b) \in S}\left(\omega^a-\zeta^b\right).
Let \omega=e^{\frac{2 \pi i}{2017}} and \zeta=e^{\frac{2 \pi i}{2019}}. Let S=\{(a, b) \in \mathbb{Z} \mid 0 \leq a \leq 2016,0 \leq b \leq 2018,(a, b) \neq(0,0)\}. Compute \prod_{(a, b) \in S}\left(\omega^a-\zeta^b\right).