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

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.