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, ..., u_k that there are edges (u_1, v), (u_2, v), ..., (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.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 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 ≤ n ≤ 2 ⋅ 10^5; 1 ≤ 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 ≤ x_i, y_i ≤ 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 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

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

Example

Input


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

Note

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

<image>

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:

<image>

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:

<image>

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.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
import java.util.stream.Collectors;

public class Solution extends Thread {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

    private static final FastReader scanner = new FastReader();
    private static final PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        new Thread(null, new Solution(), "Main", 1<<26).start();
    }

    public void run() {
        int t = scanner.nextInt();
        for (int i = 0; i < t; i++) {
            solve();
        }
        out.close();
    }

    static class Edge {
        int from;
        int to;
        boolean isDirected;

        public Edge(int from, int to, boolean isDirected) {
            this.from = from;
            this.to = to;
            this.isDirected = isDirected;
        }

        void setDirection(int from, int to) {
            this.from = from;
            this.to = to;
            isDirected = true;
        }

        @Override
        public String toString() {
            return from + " " + to;
        }
    }

    static class Node {
        int index;
        boolean visited;
        int amountNeighborLeaves = 0;
        int amountNeighbors = 0;
        List<Node> neighbors = new ArrayList<>();

        public Node(int index) {
            this.index = index;
            this.visited = false;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (!(o instanceof Node)) {
                return false;
            }
            Node node = (Node) o;
            return index == node.index;
        }

        @Override
        public int hashCode() {
            return Objects.hash(index);
        }
    }

    private static void solve() {
        int n = scanner.nextInt();
        int k = scanner.nextInt();

        Node[] nodes = new Node[n];
        for (int i = 0; i < nodes.length; i++) {
            nodes[i] = new Node(i);
        }

        Node startNode = null;

        for (int i = 0; i < n - 1; i++) {
            int xi = scanner.nextInt();
            int yi = scanner.nextInt();
            nodes[xi-1].neighbors.add(nodes[yi-1]);
            nodes[xi-1].amountNeighbors++;
            nodes[yi-1].neighbors.add(nodes[xi-1]);
            nodes[yi-1].amountNeighbors++;
            if (nodes[xi-1].neighbors.size() >= 2) {
                startNode = nodes[xi-1];
            } else if (nodes[yi-1].neighbors.size() >= 2) {
                startNode = nodes[yi-1];
            }
        }

        if (startNode == null) {
            if (k == 1) {
                System.out.println(1);
            } else {
                System.out.println(0);
            }
            return;
        }

        List<Node> possibleNodesToCut = new ArrayList<>();
        dfs(startNode, possibleNodesToCut, k);
        int result = 0;
        for (Node node: possibleNodesToCut) {
            result += cut(node, k);
        }
        System.out.println(result);
    }

    private static int cut(Node node, int k) {
        if (node.amountNeighborLeaves >= k) {

            int moves = node.amountNeighborLeaves / k;
            int restLeaves = node.amountNeighborLeaves % k;
            node.amountNeighborLeaves = restLeaves;

            if (restLeaves == 0 && node.neighbors.size() == 1) {
                node.neighbors.get(0).amountNeighborLeaves++;
                node.neighbors.get(0).neighbors.remove(node);
                moves += cut(node.neighbors.get(0), k);
            }
            return moves;
        } else {
            return 0;
        }
    }

    private static boolean dfs(Node node, List<Node> possibleNodesToCut, int k) {
        if (node.visited) {
            return false;
        }

        if (node.neighbors.size() == 1) {
            return true;
        }

        node.visited = true;
        List<Node> newNeighbors = new ArrayList<>();
        for (Node neighbor: node.neighbors) {
            boolean isLeave = dfs(neighbor, possibleNodesToCut, k);
            if (isLeave) {
                node.amountNeighborLeaves++;
            } else {
                newNeighbors.add(neighbor);
            }
        }
        node.neighbors = newNeighbors;

        if (node.amountNeighborLeaves >= k) {
            possibleNodesToCut.add(node);
        }
        return false;
    }

}











