K Forests

Chef is given a tree with $N$ nodes and a positive integer $K$. Each node is assigned a value $A_i$. Chef has to divide the tree into a forest of exactly $K$ trees, numbered from $1$ to $K$, such that each node belongs to **exactly one** tree. Let $B_i$ denote the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of the values of all nodes belonging to the $i^{th}$ tree. Fi