An implementation of a queue Q$,$ using stacks S$1$ and S$2,$ is given below

void insert$($Q$,$ x$)\{$

push $($S$1,$ x$)$;

$\}$

void delete$($Q$)\{$

if$($stack$-$empty$($S$2))$ then

if$($stack$-$empty$($S$1))$ then $\{$

print$($Q is empty$)$;

return;

$\}$

else while $(!($stack$-$empty$($S$1)))\{$

x$=$pop$($S$1)$;

push$($S$2,$x$)$;

$\}$

x$=$pop$($S$2)$;

$\}$

Let n insert and m $(<=$n$)$ delete operations be performed in an arbitrary order on an empty queue Q$.$ Let x and y be the number of push and pop operations performed respectively in the process. Which one of the following is true for all m and n$?$

Group of answer choices

n$+$m$<=$x$<2$n and $2$m$<=$y$<=$n$+$m

$2$m$<=$x$<2$n and $2$m$<=$y$<=$n$+$m

$2$m$<=$x$<2$n and $2$m$<=$y$<=2$n

n$+$m$<=$x$<2$n and $2$m$<=$y$<=2$n