Mex On Subtrees

You are given a [rooted tree](https://en.wikipedia.org/wiki/Tree_(graph_theory)#Rooted_tree) with $N$ nodes numbered from $1$ to $N$. The root of the tree is node $1$. The $i^{th}$ node has parent $P_i$ for all $2 \le i \le N$. You need to assign a value to each of the nodes such that the [MEX](https://en.wikipedia.org/wiki/Mex_(mathematics)) of the subtree of node $i$ is $B_i$. Note that the $M