Tree Separator

Time Limit : 2 sec, Memory Limit : 524288 KB

Tree Separator

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.

Input

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

$N$ $K$
$u_1$ $v_1$
:
$u_{N-1}$ $v_{N-1}$

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

Output

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

Sample Input 1

2 1
1 2

Output for Sample Input 1

0

Sample Input 2

7 3
1 2
2 3
3 4
4 5
5 6
6 7

Output for Sample Input 2

1

Sample Input 3

12 2
1 2
2 3
3 4
4 5
3 6
6 7
7 8
8 9
6 10
10 11
11 12

Output for Sample Input 3

4

Sample Input 4

3 1
1 2
2 3

Output for Sample Input 4

1

Sample Input 5

3 2
1 2
2 3

Output for Sample Input 5

0

Sample Input 6

9 3
1 2
1 3
1 4
4 5
4 6
4 7
7 8
7 9

Output for Sample Input 6

2

Source: JAG Practice Contest for ACM-ICPC Asia Regional 2017 , Japan, 2017-11-19
http://acm-icpc.aitea.net/
https://jag2017autumn.contest.atcoder.jp/