please answer the question for b$)$ and c$)$ like the diagram provided for

a$)$

$1.($AU ex$.11\mathrm{.}6\mathrm{.}1)$ Recall the program in AU$,$ fig. $11\mathrm{.}27$:

TREE B$()$

$\{$

TREE firstB, secondB;

if$(*$nextTerminal $==\text{'}(\text{'})\{/*$ follow production $2*/$

nextTerminal$++$ ;

firstB $=$ B$()$ ;

if$($ firstB $!=$ FAILED && $*$nextTerminal $==\text{'})\text{'})\{$

nextTerminal$++$ ;

secondB $=$ B$()$ ;

if$($ secondB $==$ FAILED $)$

return FAILED ;

else

return makeNode$4($

$\text{'}$B$\text{'},$

makeNode$0(\text{'}(\text{'}),$

firstB,

makeNode$0(\text{'})\text{'}),$

secondB

$)$;

$\}$

else $/*$ first call to B failed $*/$

$\}$

return FAILED ;

else $/*$ follow production $1*/$

return makeNode$1(\text{'}$B$\text{'},$ makeNode$0(\text{'}$e$\text{'}))$ ;

$\}$

Show the sequence of calls made by the program of Fig. $11\mathrm{.}27$ on the inputs:

a$.(())$

b$.(()())$

c$.())($

$($Each string is followed by the endmarker symbol, ENDM$)$