$5.$ Range$-$Search Reporting in BST: LetT be a given BST$.$ We are also given a pair of key values a and b$,$ a $<$ b $($not necessarily in T$).$ We want to report every item x in T such that a $<=$ key$[$x$]<=$ b$.$ Design an algorithm that solves the problem and takes O$($h$+$R$)$ time in the worst case, where his the height of T and R is the number of reported items $($i$.$e$.,$ the output size$).$ Prove the correctness of your algorithm and the claimed time complexity.

$[$Hint: there is a short and elegant recursive solution.$]$