Fire Extinguisher Placement

Byteasar has built a new palace with n chambers and n-1 corridors. The corridors connect the chambers so that they form a tree, with chamber 1 being the unique entrance. The fire marshal requires that fire extinguishers be placed in some of the chambers. The rules are as follows:

• Fire extinguishers can be placed in any chambers; a chamber may store any number of them.
• Every chamber must be assigned one extinguisher (which may be stored in a different chamber).
• Each extinguisher can be assigned to at most S chambers.
• For every chamber, its assigned extinguisher must be within K corridors (i.e. the distance in the tree is at most K).

Byteasar wants to use the minimum number of extinguishers to meet these requirements. Given the structure of the palace, your task is to determine that minimum number.

Note: Any formulas should be formatted in LaTeX. For example, the number of chambers is given by $n$, the capacity of each extinguisher is $S$, and the maximum allowed distance is $K$.

inputFormat

The first line contains three integers: n ($1 \le n \le 10^5$), S and K, where $n$ is the number of chambers, $S$ is the maximum number of chambers that one extinguisher can be assigned to, and $K$ is the maximum allowed distance (in number of corridors).

Each of the next n-1 lines contains two integers u and v ($1 \le u,v \le n$) describing a corridor connecting chamber u and chamber v. It is guaranteed that the palace forms a tree with chamber 1 as the entrance and that every chamber is reachable by exactly one simple path from chamber 1.

outputFormat

Output a single integer, the minimum number of fire extinguishers needed.

sample

3 1 1
1 2
1 3

3