i have a problem as follow Given a tree with n nodes with unique value for each node and q queries as given two nodes a and b ,find Mex in the path from a to b for each query

(1<n,q<200000)

my solution is using Mo algorithm as mentioned Here. i can find the Mex either using segment tree or set with log(n) for each query,but i think it is a bit hard for my solution to be valid under this constraints .

is there another solution with a better time complexity ?