If $\alpha=(3714), \beta=(123)$, and $y=(24135)$ in $S_{7}$, express each of the following as a product of disjoint cycles:
(a) $\alpha^{-1} \beta$
(b) $y^{-1} \alpha$
(c) $\alpha^{2} \beta$
$(d) \beta^{2} \alpha \gamma$
(e) $\gamma^{4}$
$(f) \gamma^{3} \alpha^{-1}$
(g) $\beta^{-1} \gamma$
$(h) \alpha^{-1} \gamma^{2} \alpha$