F. Removing Leavestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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).OutputFor each test case, print the answer — the maximum number of moves you can perform if you remove leaves optimally.ExampleInput
4
8 3
1 2
1 5
7 6
6 8
3 1
6 4
6 1
10 3
1 2
1 10
2 3
1 5
1 6
2 4
7 10
10 9
8 10
7 2
3 1
4 5
3 6
7 4
1 2
1 4
5 1
1 2
2 3
4 3
5 3
Output
2
3
3
4
NoteThe 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.
4
8 3
1 2
1 5
7 6
6 8
3 1
6 4
6 1
10 3
1 2
1 10
2 3
1 5
1 6
2 4
7 10
10 9
8 10
7 2
3 1
4 5
3 6
7 4
1 2
1 4
5 1
1 2
2 3
4 3
5 3

2 3 3 4 
['data structures', 'greedy', 'implementation', 'trees', '*2300']