Problem: Note that the only difference between the easy and hard version is the constraint on the number of queries. You can make hacks only if all versions of the problem are solved.

This is an interactive problem.

You are given a tree consisting of n nodes numbered with integers from 1 to n. Ayush and Ashish chose two secret distinct nodes in the tree. You need to find out both the nodes. You can make the following query: 

  * Provide a list of nodes and you will receive a node from that list whose sum of distances to both the hidden nodes is minimal (if there are multiple such nodes in the list, you will receive any one of them). You will also get the sum of distances of that node to the hidden nodes. 



Recall that a tree is a connected graph without cycles. The distance between two nodes is defined as the number of edges in the simple path between them.

More formally, let's define two hidden nodes as s and f. In one query you can provide the set of nodes \\{a_1, a_2, …, a_c\} of the tree. As a result, you will get two numbers a_i and dist(a_i, s) + dist(a_i, f). The node a_i is any node from the provided set, for which the number dist(a_i, s) + dist(a_i, f) is minimal.

You can ask no more than 14 queries.

Input

The first line contains a single integer t (1 ≤ t ≤ 10) — the number of test cases. Please note, how the interaction process is organized.

The first line of each test case consists of a single integer n (2 ≤ n ≤ 1000) — the number of nodes in the tree.

The next n - 1 lines consist of two integers u, v (1 ≤ u, v ≤ n, u ≠ v) — the edges of the tree.

Interaction

To ask a query print a single line: 

  * In the beginning print "? c " (without quotes) where c (1 ≤ c ≤ n) denotes the number of nodes being queried, followed by c distinct integers in the range [1, n] — the indices of nodes from the list. 



For each query, you will receive two integers x, d — the node (among the queried nodes) with the minimum sum of distances to the hidden nodes and the sum of distances from that node to the hidden nodes. If the subset of nodes queried is invalid or you exceeded the number of queries then you will get x = d = -1. In this case, you should terminate the program immediately.

When you have guessed the hidden nodes, print a single line "! " (without quotes), followed by two integers in the range [1, n] — the hidden nodes. You can output the hidden nodes in any order.

After this, you should read a string. If you guess the nodes correctly, you will receive the string "Correct". In this case, you should continue solving the remaining test cases or terminate the program, if all test cases were solved. Otherwise, you will receive the string "Incorrect". In this case, you should terminate the program immediately.

Guessing the hidden nodes does not count towards the number of queries asked.

The interactor is not adaptive. The hidden nodes do not change with queries.

Do not forget to read the string "Correct" / "Incorrect" after guessing the hidden nodes.

You need to solve each test case before receiving the input for the next test case.

The limit of 14 queries applies to each test case and not to the entire input.

After printing a query do not forget to output the end of the line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

  * fflush(stdout) or cout.flush() in C++;
  * System.out.flush() in Java;
  * flush(output) in Pascal;
  * stdout.flush() in Python;
  * see the documentation for other languages.



Hacks

To hack the solution, use the following test format:

The first line should contain a single integer t (1 ≤ t ≤ 10) — the number of test cases. The description of the test cases follows.

The first line of each test case should contain a single integer n (2 ≤ n ≤ 1000) — the number of nodes in the tree. The second line should contain two distinct integers in the range [1, n] — the hidden nodes. The next n - 1 lines should contain two integers u, v (1 ≤ u, v ≤ n, u ≠ v) — the edges of the tree.

Example

Input


1
3
1 2
1 3

1 1

2 3

3 1

3 1

Correct

Output


? 1 1

? 1 2

? 1 3

? 2 2 3

! 1 3

Note

The tree from the first test is shown below, and the hidden nodes are 1 and 3.

<image>

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class F {

    List<List<Integer>> tree = new ArrayList<>();
    int[] parent = new int[1023];

    int root, dist;

    List<Integer> query = new ArrayList<>();

    void send() {
        out.print("? " + query.size());
        for (int v : query) {
            out.print(" " + (v + 1));
        }
        out.println();
        out.flush();
    }

    void initParents(int u, int p) {
        parent[u] = p;
        for (int v : tree.get(u)) {
            if (v != p) {
                initParents(v, u);
            }
        }
    }

    int calcDepth(int u, int d) {
        int depth = d;
        for (int v : tree.get(u)) {
            if (v != parent[u]) {
                depth = Math.max(depth, calcDepth(v, d + 1));
            }
        }
        return depth;
    }

    void collectQuery(int u, int d) {
        if (d == 0) {
            query.add(u);
            return;
        }
        for (int v : tree.get(u)) {
            if (v != parent[u]) {
                collectQuery(v, d - 1);
            }
        }
    }

    int findFirst() throws IOException {
        int u = root;
        int depth = calcDepth(u, 1);
        while (depth > 1) {
            query.clear();
            collectQuery(u, depth / 2);
            send();
            int x = in.readInt() - 1;
            int d = in.readInt();
            if (d == -1) {
                exit();
            }
            d = (d - dist) / 2;
            if (d > 0) {
                for (int v : query) {
                    int w = v;
                    int l = d;
                    while (l-- > 1) {
                        w = parent[w];
                    }
                    tree.get(parent[w]).remove(Integer.valueOf(w));
                    if (v == x) {
                        u = parent[w];
                    }
                }
            } else {
                u = x;
            }
            depth = calcDepth(u, 1);
        }
        return u;
    }

    void solve() throws IOException {
        in = new InputReader("__std");
        out = new OutputWriter("__std");

        int testCount = in.readInt();
        for (int test = 1; test <= testCount; ++test) {
            int n = in.readInt();
            tree.clear();
            query.clear();
            for (int u = 0; u < n; ++u) {
                tree.add(new ArrayList<>());
                query.add(u);
            }
            for (int i = 0; i < n - 1; ++i) {
                int u = in.readInt() - 1;
                int v = in.readInt() - 1;
                tree.get(u).add(v);
                tree.get(v).add(u);
            }
            send();
            root = in.readInt() - 1;
            dist = in.readInt();
            if (dist == -1) {
                exit();
            }
            initParents(root, -1);
            int first = findFirst();
            int u = first;
            int d = 1;
            while (parent[u] != root) {
                u = parent[u];
                ++d;
            }
            tree.get(root).remove(Integer.valueOf(u));
            query.clear();
            collectQuery(root, dist - d);
            int second;
            if (query.size() > 1) {
                send();
                second = in.readInt() - 1;
                d = in.readInt();
                if (d == -1) {
                    exit();
                }
            } else {
                second = query.get(0);
            }
            out.println("! " + (first + 1) + " " + (second + 1));
            out.flush();
            if (in.readToken().equals("Incorrect")) {
                exit();
            }
        }

        exit();
    }

    void exit() {
        out.close();
        //System.err.println((System.currentTimeMillis() - startTime) + " ms");
        System.exit(0);
    }

    InputReader in;
    OutputWriter out;

    //long startTime = System.currentTimeMillis();

    public static void main(String[] args) throws IOException {
        new F().solve();
    }

    class InputReader {

        private InputStream stream;

        private byte[] buffer = new byte[1024];
        private int pos, len;

        private int cur;

        private StringBuilder sb = new StringBuilder(32);

        InputReader(String name) throws IOException {
            if (name.equals("__std")) {
                stream = System.in;
            } else {
                stream = new FileInputStream(name);
            }
            cur = read();
        }

        private int read() throws IOException {
            if (len == -1) {
                throw new EOFException();
            }
            if (pos >= len) {
                pos = 0;
                len = stream.read(buffer);
                if (len == -1) return -1;
            }
            return buffer[pos++] & 0xff;
        }

        boolean whitespace() {
            return cur == ' ' || cur == '\t' || cur == '\r' || cur == '\n' || cur == -1;
        }

        boolean eol() {
            return cur == '\r' || cur == '\n' || cur == -1;
        }

        boolean eof() {
            return cur == -1;
        }

        byte readByte() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            byte res = (byte) cur;
            cur = read();
            return res;
        }

        char readChar() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            char res = (char) cur;
            cur = read();
            return res;
        }

        int readInt() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            while (whitespace()) {
                cur = read();
            }
            if (eof()) {
                throw new EOFException();
            }
            int sign = 1;
            if (cur == '-') {
                sign = -1;
                cur = read();
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
            }
            int res = 0;
            while (!whitespace()) {
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
                res *= 10;
                res += cur - '0';
                cur = read();
            }
            return res * sign;
        }

        long readLong() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            while (whitespace()) {
                cur = read();
            }
            if (eof()) {
                throw new EOFException();
            }
            int sign = 1;
            if (cur == '-') {
                sign = -1;
                cur = read();
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
            }
            long res = 0;
            while (!whitespace()) {
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
                res *= 10;
                res += cur - '0';
                cur = read();
            }
            return res * sign;
        }

        double readDouble() throws IOException {
            return Double.parseDouble(readToken());
        }

        String readToken() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            while (whitespace()) {
                cur = read();
            }
            if (eof()) {
                throw new EOFException();
            }
            sb.setLength(0);
            while (!whitespace()) {
                sb.append((char) cur);
                cur = read();
            }
            return sb.toString();
        }

        String readLine() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            sb.setLength(0);
            while (!eol()) {
                sb.append((char) cur);
                cur = read();
            }
            if (cur == '\r') {
                cur = read();
            }
            if (cur == '\n') {
                cur = read();
            }
            return sb.toString();
        }

        void skipLine() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            while (!eol()) {
                cur = read();
            }
            if (cur == '\r') {
                cur = read();
            }
            if (cur == '\n') {
                cur = read();
            }
        }
    }

    class OutputWriter {

        private PrintWriter writer;

        OutputWriter(String name) throws IOException {
            if (name.equals("__std")) {
                writer = new PrintWriter(System.out);
            } else {
                writer = new PrintWriter(name);
            }
        }

        void print(String format, Object ... args) {
            writer.print(new Formatter(Locale.US).format(format, args));
        }

        void println(String format, Object ... args) {
            writer.println(new Formatter(Locale.US).format(format, args));
        }

        void print(Object value) {
            writer.print(value);
        }

        void println(Object value) {
            writer.println(value);
        }

        void println() {
            writer.println();
        }

        void printArray(int[] a) {
            boolean first = true;
            for (int v : a) {
                if (!first) {
                    writer.print(' ');
                } else {
                    first = false;
                }
                writer.print(v);
            }
            writer.println();
        }

        void printArray(int[][] a) {
            for (int[] v : a) {
                printArray(v);
            }
        }

        void flush() {
            writer.flush();
        }

        void close() {
            writer.close();
        }
    }
}