$A$ radioactive nucleus ${}_{Z}^{A}X$ undergoes spontaneous decay in the sequence ${}_{Z}^{A}X \rightarrow {}_{Z-1}B \rightarrow {}_{Z-3}C \rightarrow {}_{Z-2}D$,where $Z$ is the atomic number of element $X$. The possible decay particles in the sequence are:

• A
  $\alpha, \beta^{-}, \beta^{+}$
• B
  $\alpha, \beta^{+}, \beta^{-}$
• C
  $\beta^{+}, \alpha, \beta^{-}$
• D
  $\beta^{-}, \alpha, \beta^{+}$