Leaf Sets

Description:

Input:

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$3 \le n \le 10^6$$$, $$$1 \le k \le 10^6$$$) — the number of vertices in the tree and the maximum distance between any pair of leaves in each beautiful set.

Each of the next $$$n - 1$$$ lines contains two integers $$$v_i$$$ and $$$u_i$$$ ($$$1 \le v_i, u_i \le n$$$) — the description of the $$$i$$$-th edge.

It is guaranteed that the given edges form a tree.

Output:

Print a single integer — the minimal number of beautiful sets the split can have.

Sample Input:

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

Sample Output:

2

Sample Input:

5 3
1 2
2 3
3 4
4 5

Sample Output:

2

Sample Input:

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

Sample Output:

5

Note:

Here is the graph for the first example: