Tree Cutting

A tree is a connected graph with no cycles. Cutting one edge of a tree splits it into two trees.

You are given a tree with n vertices. Cut some edges so that at least one remaining connected component is a tree with exactly m vertices. Find the minimum number of edges that must be cut.

The first line contains n (1 ≤ n ≤ 150) and m (1 ≤ m ≤ n). Each of the next n-1 lines contains two integers A and B describing an edge of the tree. This means that vertex A and vertex B are connected.

Print the minimum number of edges that must be cut to obtain a tree with exactly m vertices. If it cannot be done, print -1.