15522번 - Tree Separator 다국어

You are given a tree T and an integer K. You can choose arbitrary distinct two vertices u and v on T. Let P be the simple path between u and v. Then, remove vertices in P, and edges such that one or both of its end vertices is in P from T. Your task is to choose u and v to maximize the number of connected components with K or more vertices of T after that operation.

The input consists of a single test case formatted as follows.

N K
u1 v1
.
.
.
uN-1 vN-1

The first line consists of two integers N, K (2 ≤ N ≤ 100,000, 1 ≤ K ≤ N). The following N-1 lines represent the information of edges. The (i+1)-th line consists of two integers u_i, v_i (1 ≤ u_i, v_i ≤ N and u_i ≠ v_i for each i). Each {u_i, v_i} is an edge of T. It's guaranteed that these edges form a tree.

Print the maximum number of connected components with K or more vertices in one line.