Specify, design, and implement a class for binary trees where the node’s elements are stored in an array, similar to the way that a complete binary tree is usually stored. However, these binary trees do not need to be complete. Instead, you should have a second private instance variable that is an array of boolean values called isPresent. The isPresent array indicates which nodes actually exist in the tree. For example, if the tree has a root node, then isPresent[0] is true. If the root has a left child, then isPresent[1] is true. If the root has a right child, then isPresent[2] is true, and so on.

The class should have methods to create the first node and to move a cursor around the tree. After the first node, new nodes may be added only as children of the cursor.