A tree can be uniquely determined by specifing its postorder sequence and number of leaves for each node.

Let's consider a tree with the following postorder sequence of its nodes and corresponding number of children:

nodes: J$-$H$-$A$-$E$-$I$-$G$-$K$-$C$-$B$-$F$-$D

number of leaves: $0-0-0-3-0-0-0-0-3-2-2$

$($for example, the node $E$ has $3$ children and the node $G$ is a leaf$)$

Which of the following is the preorder traversal sequence of this tree?

D$-$E$-$F$-$H$-$K$-$I$-$F$-$B$-$G$-$A$-$C

D$-$I$-$C$-$H$-$A$-$G$-$E$-$B$-$F$-$K$-$J

I$-$E$-$A$-$H$-$J$-$F$-$D$-$B$-$G$-$K$-$C

D$-$A$-$J$-$H$-$E$-$K$-$I$-$B$-$E$-$F$-$C

D$-$E$-$J$-$H$-$A$-$F$-$I$-$B$-$G$-$K$-$C

D$-$F$-$J$-$B$-$G$-$E$-$I$-$H$-$A$-$K$-$C

A$-$E$-$J$-$F$-$D$-$H$-$B$-$I$-$G$-$K$-$C

D$-$E$-$H$-$J$-$A$-$J$-$I$-$B$-$G$-$F$-$C

C$-$E$-$K$-$H$-$A$-$J$-$I$-$B$-$G$-$J$-$D

A$-$E$-$C$-$H$-$D$-$I$-$F$-$B$-$G$-$K$-$J

C$-$G$-$J$-$H$-$A$-$F$-$I$-$B$-$D$-$K$-$D