CF372D.Choosing Subtree is Fun

There is a tree consisting of $n$ vertices. The vertices are numbered from $1$ to $n$ .

Let's define the length of an interval $[l,r]$ as the value $r-l+1$ . The score of a subtree of this tree is the maximum length of such an interval $[l,r]$ that, the vertices with numbers $l,l+1,...,r$ belong to the subtree.

Considering all subtrees of the tree whose size is at most $k$ , return the maximum score of the subtree. Note, that in this problem tree is not rooted, so a subtree — is an arbitrary connected subgraph of the tree.

There are two integers in the first line, $n$ and $k$ ( $1<=k<=n<=10^{5}$ ). Each of the next $n-1$ lines contains integers $a_{i}$ and $b_{i}$ ( $1<=a_{i},b_{i}<=n,a_{i}≠b_{i}$ ). That means $a_{i}$ and $b_{i}$ are connected by a tree edge.

It is guaranteed that the input represents a tree.

Output should contain a single integer — the maximum possible score.

For the first case, there is some subtree whose size is at most $6$ , including $3$ consecutive numbers of vertices. For example, the subtree that consists of ${1,3,4,5,7,8}$ or of ${1,4,6,7,8,10}$ includes $3$ consecutive numbers of vertices. But there is no subtree whose size is at most $6$ , which includes $4$ or more consecutive numbers of vertices.