Consider the function e as defined in the following SML code.

fun $ea([],ys)=ys$

$|$e a $((x$::$xs),ys)=$ if $a=x$ then e $(a+1)(xs,(x$::$ys))$ else e a $($xs$,$ys$)$;

What is the type of $e?$

None of the other answers are correct.

$"$a $->"$b list $*"$b list $->$ "a list

int $$ int list $*$ int list $$ int list

$"$a $*$ "a list $->$ "a list

int $*($int list $*$ int list$)->$ int list