We define an AVL binary search tree to be a tree with the binary search tree property where, for each node in the tree, the height of its children differs by no more than 1. For this problem, assume we have a team of biologists that keep information about DNA sequences in an AVL binary search tree using the specific weight (an integer) of the structure as the key. The biologists routinely ask questions of the type, Are there any structures in the tree with specific weight between a and b, inclusive? and they hope to get an answer as soon as possible. Design an efficient algorithm that, given integers a and b, returns true if there exists a key x in the tree such that a x b, and false if no such key exists in the tree. Describe your algorithm in pseudocode and English. What is the time complexity of your algorithm? Explain.