Given a tree with ~n~ vertices. Edge ~i~ of the tree has length ~l_i~. We need to choose ~m~ edge-disjoint paths such that the length of the path with minimum length is maximized.

Input Specification

The first line contains two integers ~n~ and ~m~ denoting the number of vertices and the number of paths to be chosen.

In the following ~n-1~ lines, the ~i^\text{th}~ line contains three positive integers ~a_i, b_i, l_i~ denoting the ~i^\text{th}~ edge goes from ~a_i~ to ~b_i~ and has length ~l_i~.

Output Specification

The output contains an integer denoting the maximum possible minimum length of the ~m~ tracks chosen.

Sample Input 1

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

Sample Output 1

31

Note: the chosen path is the path from vertex 4 to vertex 7.

Sample Input 2

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

Sample Output 2

15

The chosen paths are the path from vertex 1 to vertex 7, vertex 6 to vertex 9, and vertex 8 to vertex 5.

Additional Samples

Additional samples can be found here.

Constraints

Test Case	~n \le~	~m~	~a_i = 1~	~b_i = a_i+1~	Degree of vertex ~\le 3~
1	~5~	~= 1~	No	No	Yes
2	~10~	~\le n-1~		Yes
3	~15~		Yes	No	No
4	~1\,000~	~= 1~	No		Yes
5	~30\,000~		Yes		No
6			No
7		~\le n-1~	Yes
8	~50\,000~
9	~1\,000~		No	Yes	Yes
10	~30\,000~
11	~50\,000~
12	~50~			No
13
14	~200~
15
16	~1\,000~
17					No
18	~30\,000~
19
20	~50\,000~

For all test cases, ~2 \le n \le 50\,000~, ~1 \le m \le n-1~, ~1 \le a_i,b_i \le n~, ~1 \le l_i \le 10\,000~.