Show that EAV$2-$security can be achieved by encryption schemes defined over messages up to a given maximum length, i$.$e$.,$ by schemes $\backslash$Pi $0$ such that for k in $\{0,1\}$n$,$ algorithm Enc$0$k is defined over message space M$0=\{$m : $|$m$|<=`\},$ where $`,`($n$)$ for some given polynomial $`().$

Hint: Construct a scheme $\backslash$Pi $)$ that encrypts messages in M$0$ by employing a EAV$-$secure scheme $\backslash$Pi $=($Gen$,$Enc,Dec$)$ with message space M$.$ Consider an algorithm Enc$0$ that on input message m$0$ in M$0,$ merely applies Enc on a unique and inversible encoding m $=$ E$($m$0)$ in M of m$0$ in a way that $$compensates$$ for the absence of the restriction $|$m$0|=|$m$1|$ in game PrivK$-$EAV$2$A$,\backslash$Pi $0($n$).$ Then, prove that $\backslash$Pi $0$ is EAV$2-$secure via a proof by reduction.