Lost in Binary Tree

You have a rooted unweighted binary tree. But somehow you forgot which vertex was the root. Well, you can ask me. I remember. But let's play a game. In each move, you can pick a vertex and ask me the distance of that vertex from that root. And I'll tell you so. However, I'll answer no more than 202020 of your queries.

This is a companion discussion topic for the original entry at https://toph.co/p/lost-in-binary-tree