Find Path Between Fibonacci Tree Nodes

You are given a special family of binary trees called **Fibonacci trees**. Define the tree `T(k)` recursively: - `T(1)` is a single node. - `T(2)` is a single node. - For `k >= 3`, `T(k)` consists of a root node whose: - left subtree is `T(k - 1)` - right subtree is `T(k - 2)` Let `size(k)` be the number of nodes in `T(k)`: - `size(1) = 1` - `size(2) = 1` - `size(k) = 1 + size(k - 1) + size(k - 2)` for `k >= 3` Now number all nodes of `T(k)` using **preorder traversal** (`root -> left -> right`) with **1-based indices** from `1` to `size(k)`. Given: - an integer `k` where `1 <= k <= 60` - two preorder indices `a` and `b` such that `1 <= a, b <= size(k)` Implement a function: `List<Long> pathInFibonacciTree(long k, long a, long b)` Return the sequence of preorder indices along the unique simple path from node `a` to node `b` in `T(k)`. Requirements: - The returned list must start with `a` and end with `b`. - The tree may be extremely large, so you must **not** construct the full tree explicitly in memory. - Your algorithm should determine the path using only the recursive structure of the Fibonacci tree.