Find out the major products $A$ and $B$ from the following reaction sequence.

  • A
    $A$ = $4-$chlorophenyl$-2-$hydroxy$-2-$methylacetic acid,$B$ = $1-$($4$-chlorophenyl)$-1,2-$dihydroxy$-2-$methylpropane derivative
  • B
    $A$ = ethyl $2-$($4$-chlorophenyl)$-2-$hydroxypropanoate,$B$ = $2-$($4$-chlorophenyl)$-3-$methylbutane$-2,3-$diol
  • C
    $A$ = $2-$($4$-chlorophenyl)$-2-$hydroxypropanenitrile,$B$ = $2-$($4$-chlorophenyl)$-3-$methylbutane$-2,3-$diol
  • D
    $A$ = $2-$($4$-cyanophenyl)$-2-$hydroxypropanenitrile,$B$ = $1-$($4$-chlorophenyl)$-1,2-$dihydroxy$-2-$methylpropane derivative

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