Tree Upshot

You are given a tree with $N$ nodes rooted at node $1$, and your task is to color each node of the tree either white or black. For each $i$ ($1 \leq i \leq N$), let $w_i$ be the number of white nodes that occurs in a simple path from the root node to $i^{th}$ node and $b_i$ be the number of black nodes that occurs in a simple path from the root node to $i^{th}$ node. The cost of a node $i$ is defi