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.

给你一棵树（即无环的连通图），该树包含 $n$ 个顶点。这棵树是无根的——它仅仅是一个无环的无向连通图。

在一次操作中，你可以恰好选择 $k$ 个叶子节点（叶子节点指仅与另一个顶点相连的顶点），且这些叶子节点必须全部连接到同一个顶点，然后将这些叶子节点及其关联的边一并删除。换言之，你选择叶子节点 $u_1, u_2, \dots, u_k$，使得存在边 $(u_1, v)$、$(u_2, v)$、$\dots$、$(u_k, v)$，然后将这些叶子节点及对应边全部移除。

你的任务是：在最优地删除叶子节点的前提下，求出最多能执行多少次这样的操作。

你需要回答 $t$ 个相互独立的测试用例。

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 $k$ ($2 \le n \le 2 \cdot 10^5$; $1 \le k \lt n$) — 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 $2 \cdot 10^5$ ($\sum n \le 2 \cdot 10^5$).

输入的第一行包含一个整数 $t$（$1 \le t \le 2 \cdot 10^4$），表示测试用例的数量。随后是 $t$ 个测试用例。

每个测试用例的第一行包含两个整数 $n$ 和 $k$（$2 \le n \le 2 \cdot 10^5$；$1 \le k \lt n$），分别表示树中顶点的数量以及每次操作中要删除的叶子节点数量。接下来的 $n-1$ 行描述树的边。第 $i$ 条边由两个整数 $x_i$ 和 $y_i$（$1 \le x_i, y_i \le n$）表示，即该边连接顶点 $x_i$ 和 $y_i$。保证所给边集构成一棵树。

保证所有测试用例的 $n$ 值之和不超过 $2 \cdot 10^5$（即 $\sum n \le 2 \cdot 10^5$）。

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

对于每个测试用例，输出答案——即在最优地移除叶子节点的情况下，你能执行的最大移动次数。

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.

示例中第一个测试用例对应的图片：

在此图中，你可以在第一轮操作中移除顶点 $2$、$5$ 和 $3$，在第二轮操作中移除顶点 $1$、$7$ 和 $4$。

示例中第二个测试用例对应的图片：

在此图中，你可以在第一轮操作中移除顶点 $7$、$8$ 和 $9$，第二轮操作中移除顶点 $5$、$6$ 和 $10$，第三轮操作中移除顶点 $1$、$3$ 和 $4$。

示例中第三个测试用例对应的图片：

在此图中，你可以在第一轮操作中移除顶点 $5$ 和 $7$，第二轮操作中移除顶点 $2$ 和 $4$，第三轮操作中移除顶点 $1$ 和 $6$。