There are $n$ cities and $n-1$ roads between them. There is a unique route between any two cities, and their distance is the number of roads on that route.
A company wants to have offices in some cities, but the distance between any two offices has to be at least $d$ . What is the maximum number of offices they can have?
The first input line has two integers $n$ and $d$ : the number of cities and the minimum distance. The cities are numbered $1,2,\dots,n$ .
After this, there are $n-1$ lines describing the roads. Each line has two integers $a$ and $b$ : there is a road between cities $a$ and $b$ .
First print an integer $k$ : the maximum number of offices. After that, print the cities which will have offices. You can print any valid solution.
5 3 1 2 2 3 3 4 3 5· \n · \n · \n · \n · \n
2 1 4\n · \n