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	$1000$	$=1$	No		Yes
5	$30000$		Yes		No
6			No
7		$\le n-1$	Yes
8	$50000$
9	$1000$		No	Yes	Yes
10	$30000$
11	$50000$
12	$50$			No
13
14	$200$
15
16	$1000$
17					No
18	$30000$
19
20	$50000$

For all test cases, $2\le n\le 50000$, $1\le m\le n-1$, $1\le a_i,b_i\le n$, $1\le l_i\le 10000$.