- Time limit: 1.00 s
- Memory limit: 512 MB
There are cities and 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 . What is the maximum number of offices they can have?
Input
The first input line has two integers and : the number of cities and the minimum distance. The cities are numbered .
After this, there are lines describing the roads. Each line has two integers and : there is a road between cities and .
Output
First print an integer : the maximum number of offices. After that, print the cities which will have offices. You can print any valid solution.
Constraints
Example
Input:
5 3 1 2 2 3 3 4 3 5
Output:
2 1 4