Fuleco and the Ant

An ant walks the left/right perimeter of a tree; record U/D at each fork. Index $k$ is the fork after $k$ steps from the root. Output the tree distance between indices $A$ and $B$.

Line 1: $A$, $B$. Line 2: UD string $S$.

One integer distance.

$|S| < 10^6$; $S$ encodes a valid tree.