$2\mathrm{.}1-5$ Consider the problem of adding two n$-$bit binary integers a and b$,$ stored in two n$-$element arrays A$[0$:n $1]$ and B$[0$:n $1]$ and B$[0$:n $1],$ where each element is either $0$ or $1,$ a $=$ A$[$i$]2,$ and b $=$ CB$[$i$]2.$ The sum c $=$ a $+$ b of the two integers should be stored in binary form in an $($n $+1)-$element array C$[0$:n$],$ where c $=\backslash$Sigma io C$[$i$]2.$ Write a procedure ADD$-$BINARY$-$INTEGERS that takes $-1=0$ as input arrays A and B$,$ along with the length n$,$ and returns array C holding the sum.