$6)(8$ pts$)$ Write an efficient algorithm that, using Binary Search Trees, takes a list $\backslash ($ X $\backslash )$ of $\backslash ($ n $\backslash )$ integers and another integer k $,$ then find all pairs of integers in X whose sum adds up to k $.$ Implement your algorithm in Python and show how it works on three examples that cover different cases of the input data. Provide the complexity analysis of your algorithm.