A Fibonacci tree is a binary tree recursively defined as:

• T(0) is the empty tree.
• T(1) is the binary tree with only one node.
• T(k) consists of a root node that has T(k-1) and T(k-2) as children.

On such a tree two players play a take-away game. On each turn a player selects a node and removes that node along with the subtree rooted at that node.
The player who is forced to take the root node of the entire tree loses.

Here are the winning moves of the first player on the first turn for T(k) from k=1 to k=6.

For example, f(5) = 1 and f(10) = 17.

Find f(10000). Give the last 18 digits of your answer.