Tree Pruning

You are given a rooted tree with $N$ nodes in which every node has at most two children. Each node is either black or white. A prune is the operation of deleting a node together with the whole subtree rooted at that node. Given an integer $D$, find the minimum number of prunes needed to obtain a tree in which (the number of white nodes) $-$ (the number of black nodes) equals exactly $D$, or report that it is impossible.

The first line contains two integers $N$ ($1 \le N \le 300$) and $D$ ($-N \le D \le N$): the number of nodes and the required difference. The next $N$ blocks each describe one node. The first line of a block contains three integers: the id of the node (a distinct integer from $0$ to $N-1$), its colour ($1$ for white, $0$ for black), and the number of children $C$. The following $C$ lines each contain the id of one child of that node. The root of the tree is the node with id $0$.

Output, on a single line, the minimum number of prunes described above. If the required difference $D$ cannot be achieved, output $-1$.