$($a$)$ Below, write the content of a non$-$empty queue $Q$ by filling in the following blank $($with a list of integers$)$

such that calling ReverseAndRemoveOdds$($Q$)$ gives a WRONG result without raising any exception.

The size of the queue must be less than or equal to $5.$ If such an input does not exist, write

"IMPOSSIBLE" in the blank.

Q: $($fron

k$)$

$($b$)$ Below, write the content of a non$-$empty queue $Q$ by filling in the following blank $($with a list of integers$)$

such that calling ReverseAndRemoveOdds$($Q$)$ gives a CORRECT result without raising any exception.

The size of the queue must be less than or equal to $5.$ If such an input does not exist, write

"IMPOSSIBLE" in the blank.

Q: $($frc

:k$)$

$($c$)$ Below, write the content of a non$-$empty queue $Q$ by filling in the following blank $($with a list of integers$)$

such that calling ReverseAndRemoveOdds$($Q$)$ will result in a "maximum levels of recursion exceeded"

error. The size of the queue must be less than or equal to $5.$ If such an input does not exist, write

"IMPOSSIBLE" in the blank.

Q: $($front

ack$)$Below is an attempt to implement a ReverseAndRemoveOdds$($Q$)$ operation on a queue Q$.$ The method is supposed to reverse the order of the items in the queue as well as removing all the odd numbers. However, the pseudocode is buggy.

Below is an example of a queue Q before and after ReverseAndRemoveOdds$($Q$)$ if the method worked correctly.

BEFORE: $($front$)3,1,4,1,5,2,6($back$)$

AFTER: $($front$)6,2,4($back$)$

$/*$

Assume the following behaviour of the Queue methods.

Enqueue$($item$)$: enqueue at the back of the queue

Dequeue$()$: dequeue at the front. Raise an exception if the queue is empty.

IsEmpty$()$: returns whether the queue is empty.

$*/$

void ReverseAndRemoveOdds$($Q$)\{$ x $=$ Q$.$Dequeue$()$; Helper$($Q$,$ x$)$;

return;

$\}$

void Helper$($Q$,$ item$)\{$ if $($Q$.$isEmpty$())\{$

return;

$\}$

x $=$ Q$.$Dequeue$()$; Helper$($Q$,$ x$)$;

if $($item is even$)\{$ Enqueue$($item$)$;

$\}$

return;

$\}$

$($a$)$ Below, write the content of a non$-$empty queue Q by filling in the following blank $($with a list of integers$)$ such that calling ReverseAndRemoveOdds$($Q$)$ gives a WRONG result without raising any exception.

The size of the queue must be less than or equal to $5.$ If such an input does not exist, write

$$IMPOSSIBLE$$ in the blank.

Q: $($front$)($back$)$

$($b$)$ Below, write the content of a non$-$empty queue Q by filling in the following blank $($with a list of integers$)$ such that calling ReverseAndRemoveOdds$($Q$)$ gives a CORRECT result without raising any exception.

The size of the queue must be less than or equal to $5.$ If such an input does not exist, write

$$IMPOSSIBLE$$ in the blank.

Q: $($front$)($back$)$

$($c$)$ Below, write the content of a non$-$empty queue Q by filling in the following blank $($with a list of integers$)$ such that calling ReverseAndRemoveOdds$($Q$)$ will result in a $$maximum levels of recursion exceeded$$ error. The size of the queue must be less than or equal to $5.$ If such an input does not exist, write

$$IMPOSSIBLE$$ in the blank.

Q: $($front$)($back$)$