CF1385F.Removing Leaves

You are given a tree (connected graph without cycles) consisting of $n$ vertices. The tree is unrooted — it is just a connected undirected graph without cycles.

In one move, you can choose exactly $k$ leaves (leaf is such a vertex that is connected to only one another vertex) connected to the same vertex and remove them with edges incident to them. I.e. you choose such leaves $u_1, u_2, \dots, u_k$ that there are edges $(u_1, v)$ , $(u_2, v)$ , $\dots$ , $(u_k, v)$ and remove these leaves and these edges.

Your task is to find the maximum number of moves you can perform if you remove leaves optimally.

You have to answer $t$ independent test cases.

The first line of the input contains one integer $t$ ( $1 \le t \le 2 \cdot 10^4$ ) — the number of test cases. Then $t$ test cases follow.

The first line of the test case contains two integers $n$ and $k$ ( $2 \le n \le 2 \cdot 10^5$ ; $1 \le k < n$ ) — the number of vertices in the tree and the number of leaves you remove in one move, respectively. The next $n-1$ lines describe edges. The $i$ -th edge is represented as two integers $x_i$ and $y_i$ ( $1 \le x_i, y_i \le n$ ), where $x_i$ and $y_i$ are vertices the $i$ -th edge connects. It is guaranteed that the given set of edges forms a tree.

It is guaranteed that the sum of $n$ does not exceed $2 \cdot 10^5$ ( $\sum n \le 2 \cdot 10^5$ ).

For each test case, print the answer — the maximum number of moves you can perform if you remove leaves optimally.

The picture corresponding to the first test case of the example:

There you can remove vertices $2$ , $5$ and $3$ during the first move and vertices $1$ , $7$ and $4$ during the second move.

The picture corresponding to the second test case of the example:

There you can remove vertices $7$ , $8$ and $9$ during the first move, then vertices $5$ , $6$ and $10$ during the second move and vertices $1$ , $3$ and $4$ during the third move.

The picture corresponding to the third test case of the example:

There you can remove vertices $5$ and $7$ during the first move, then vertices $2$ and $4$ during the second move and vertices $1$ and $6$ during the third move.