Subtree Domination

You are given a tree consisting of $N$ vertices, numbered from $1$ to $N$. For a fixed root vertex $r$, let $\operatorname{subsize}_r(u)$ denote the number of vertices in the subtree of $u$ when the tree is rooted at $r$. Formally, this is the count of vertices $v$ such that $u$ lies on the simple path between $r$ and $v$ in the tree. For two vertices $u$ and $v$, define $f(u,v)$ as the number