Queries on a Binary Tree

Let's consider a rooted binary tree with the following properties: - The number of nodes and edges in the tree is infinite - The tree root is labeled by $1$ - A node labeled by $v$ has two children: $2 \cdot v$ (the left child of $v$), and $2 \cdot v + 1$ (the right child of $v$). Here is an image of the first several layers of such a tree: Let's consider four operations that you are allowe