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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.stream.IntStream;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.function.Function;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Map;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.Collection;
import java.util.Set;
import java.io.IOException;
import java.util.stream.Collectors;
import java.util.List;
import java.util.stream.Stream;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author out_of_the_box
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DGuessTheMaximums solver = new DGuessTheMaximums();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class DGuessTheMaximums {
        private Map<Set<Integer>, Integer> cache;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            cache = new HashMap<>();
            int n = in.nextInt();
            int k = in.nextInt();
            int maxNodVal;
            List<List<Integer>> subs = new ArrayList<>();
            List<Integer> otherList = new ArrayList<>();
            boolean[] others = new boolean[n + 1];
            for (int i = 0; i < k; i++) {
                int c = in.nextInt();
                int[] tArr = in.nextIntArray(c);
                for (int val : tArr) {
                    others[val] = true;
                }
                subs.add(Arrays.stream(tArr).boxed().collect(Collectors.toList()));
            }
            for (int i = 1; i <= n; i++) {
                if (!others[i]) {
                    otherList.add(i);
                }
            }

            maxNodVal = query(subs.stream().flatMap(List::stream).collect(Collectors.toList()), in, out);
            int mxInd;
            Function<Integer, Boolean> func =
                    ind -> (query(subs.subList(0, ind + 1).stream().flatMap(List::stream)
                            .collect(Collectors.toList()), in, out) == maxNodVal);
            if (k > 1) {
                mxInd = BinarySearch.searchFirstOne(0, k, func);
            } else {
                mxInd = 0;
            }
            if (mxInd == k) {
                throw new RuntimeException("Unexpected state. max val node is not found in array");
            }
            int[] ans = new int[k];

            if (k != 1) {
                List<Integer> allOtherNodes = IntStream.range(0, k).filter(y -> (y != mxInd)).boxed().map(subs::get)
                        .flatMap(List::stream).collect(Collectors.toList());
                List<Integer> nq = Stream.concat(allOtherNodes.stream(), otherList.stream())
                        .collect(Collectors.toList());
                int otherAns = query(nq, in, out);
                if (otherAns > maxNodVal) {
                    for (int i = 0; i < k; i++) {
                        ans[i] = otherAns;
                    }
                } else {
                    for (int i = 0; i < k; i++) {
                        if (i != mxInd) {
                            ans[i] = maxNodVal;
                        }
                    }
                    ans[mxInd] = otherAns;
                }
            } else {
                int otherAns = query(otherList, in, out);
                ans[0] = otherAns;
            }
            output(ans, in, out);
            cache.clear();
        }

        private int query(List<Integer> sub, InputReader in, OutputWriter out) {
            Set<Integer> st = new HashSet<>(sub);
            if (cache.containsKey(st)) {
                return cache.get(st);
            }
            int c = sub.size();
            out.print("? " + c);
            for (int val : sub) {
                out.print(" " + val);
            }
            out.println();
            out.println();
            out.flush();

            int x = in.nextInt();
            cache.put(st, x);
            if (x == -1) {
                throw new RuntimeException("x == -1 received");
            }

            return x;
        }

        private void output(int[] password, InputReader in, OutputWriter out) {
            out.print("!");
            for (int val : password) {
                out.print(" " + val);
            }
            out.println();
            out.flush();

            String outcome = in.nextString();
            if (outcome.equals("Incorrect")) {
                throw new RuntimeException("Incorrect assertion");
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return nextString();
        }

        public int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) array[i] = nextInt();
            return array;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

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

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

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

    }

    static class BinarySearch {
        public static int searchFirstOne(int start, int end, Function<Integer, Boolean> valueFunc) {
            int low = start;
            int high = end - 1;
            while (low < high) {
                int mid = low + (high - low) / 2;
                if (valueFunc.apply(mid)) {
                    high = mid;
                } else {
                    low = mid + 1;
                }
            }

            if (valueFunc.apply(low)) {
                return low;
            } else {
                return end;
            }
        }

    }
}