Algorithm

$1.$ Read the tree, build parent array.

$2.$ Build the $up$ table:

up[v][0] = parent[v]

up[v][j] = up[up[v][j-1]][j-1]

$3.$ For each query $(v, k)$, jump up $k$ steps using the binary lifting technique.

$4.$ If you reach an invalid node (null or past root), return $-1$.

Otherwise, return the final node.

This runs in $O(n \log n)$ preprocessing time and $O(\log n)$ per query. Space is $O(n \log n)$ for the table.