A$)$Suppose we are solving the same runway reservation system, and we received the following landing reservation requests: $45,50,55,65,75,85,87,95,97,105,115,118,121$ and $125.$ If they all satisfied the k minute difference $(3$ minutes$)$ add them in the tree in a way that we achieve the result in log$($n$)$ format. Show each step of insertion and rotation. Try to solve the problem using AVL Tree.

B$)$Solve the same single runway reservation system $(1$a$)$ using Double Hashing. Show all step and compute the time complexity of solving this problem using Double Hashing, we have no restrictions of achieving the result in log$($n$).$ If it is not solvable, do explain why