Problem: This is an interactive problem.

Ayush devised a new scheme to set the password of his lock. The lock has k slots where each slot can hold integers from 1 to n. The password P is a sequence of k integers each in the range [1, n], i-th element of which goes into the i-th slot of the lock.

To set the password of his lock, Ayush comes up with an array A of n integers each in the range [1, n] (not necessarily distinct). He then picks k non-empty mutually disjoint subsets of indices S_1, S_2, ..., S_k (S_i \underset{i ≠ j} ∩ S_j = ∅) and sets his password as P_i = max_{j ∉ S_i} A[j]. In other words, the i-th integer in the password is equal to the maximum over all elements of A whose indices do not belong to S_i.

You are given the subsets of indices chosen by Ayush. You need to guess the password. To make a query, you can choose a non-empty subset of indices of the array and ask the maximum of all elements of the array with index in this subset. You can ask no more than 12 queries.

Input

The first line of the input contains 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 contains two integers n and k (2 ≤ n ≤ 1000, 1 ≤ k ≤ n) — the size of the array and the number of subsets. k lines follow. The i-th line contains an integer c (1 ≤ c < n) — the size of subset S_i, followed by c distinct integers in the range [1, n] — indices from the subset S_i.

It is guaranteed that the intersection of any two subsets is empty.

Interaction

To ask a query print a single line: 

  * In the beginning print "? c " (without quotes) where c (1 ≤ c ≤ n) denotes the size of the subset of indices being queried, followed by c distinct space-separated integers in the range [1, n]. 



For each query, you will receive an integer x — the maximum of value in the array among all the indices queried. If the subset of indices queried is invalid or you exceeded the number of queries (for example one of the indices is greater than n) then you will get x = -1. In this case, you should terminate the program immediately.

When you have guessed the password, print a single line "! " (without quotes), followed by k space-separated integers — the password sequence.

Guessing the password does not count towards the number of queries asked.

After this, you should read a string. If you guess the password correctly, you will receive the string "Correct". In this case, you should continue solving the remaining test cases. If the guessed password is incorrect, you will receive the string "Incorrect". In this case, you should terminate the program immediately.

The interactor is not adaptive. The array A does not change with queries.

After printing a query do not forget to output end of 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 documentation for other languages.



Hacks

To hack the solution use the following test format:

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

The first line of each test case should contain two integers n and k (2 ≤ n ≤ 1000, 1 ≤ k ≤ n) — the size of the array and the number of subsets. The next line should consist of n space separated integers in the range [1, n] — the array A. k lines should follow. The i-th line should contain an integer c (1 ≤ c < n) — the size of subset S_i, followed by c distinct integers in the range [1, n] — indices from the subset S_i.

The intersection of any two subsets has to be empty.

Example

Input


1
4 2
2 1 3
2 2 4

1

2

3

4

Correct

Output


? 1 1

? 1 2

? 1 3

? 1 4

! 4 3

Note

The array A in the example is [1, 2, 3, 4]. The length of the password is 2. The first element of the password is the maximum of A[2], A[4] (since the first subset contains indices 1 and 3, we take maximum over remaining indices). The second element of the password is the maximum of A[1], A[3] (since the second subset contains indices 2, 4).

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

Solution (in JAVA):

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

public class Solution {
    public static int query(int l, int r, Scanner scan) throws IOException {
        StringBuilder sb = new StringBuilder();
        sb.append("? ");
        sb.append((r - l + 1) + " ");
        for(int i = l; i <= r; i++)
            sb.append((i + 1) + " ");
        System.out.println(sb);
        return Integer.valueOf(scan.nextLine());
    }

    public static int query2(int l, int r, int[] nums, Scanner scan) throws IOException {
        Arrays.sort(nums);
        int p = 0;

        StringBuilder sb = new StringBuilder();
        sb.append("? ");
        sb.append((r - l + 1 - nums.length) + " ");

        for(int i = l; i <= r; i++) {
            if(p < nums.length && i == nums[p]) {p++; continue;}
            sb.append((i + 1) + " ");
        }

        System.out.println(sb);
        return Integer.valueOf(scan.nextLine());
    }

    public static void main(String[] args) throws IOException {
        Scanner scan = new Scanner(System.in);
        int T = Integer.valueOf(scan.nextLine());
        for(int t = 0; t < T; t++) {
            String[] configs = scan.nextLine().split(" ");
            int N = Integer.valueOf(configs[0]); int K = Integer.valueOf(configs[1]);
            int[][] numsval = new int[K][];
            for(int k = 0; k < K; k++) {
                String[] tmp = scan.nextLine().split(" ");
                int n = Integer.valueOf(tmp[0]);
                int[] nums = new int[n];
                boolean flag = false;
                for(int i = 0; i < n; i++) {
                    nums[i] = Integer.valueOf(tmp[i + 1]) - 1;
                }
                numsval[k] = nums;
            }

            int l = 0, r = N - 1, max = query(0, r, scan);
            while(l < r) {
                int mid = (l + r) >> 1;
                int val = query(l, mid, scan);
                if(val == -1) return;
                if(val == max) r = mid;
                else l = mid + 1;
            }

//            System.out.println("l:" + l);

            int lindex = -1;
            int lmax = -1;

            for(int k = 0; k < K; k++) {
                int[] nums = numsval[k];
                int n = nums.length;
                boolean flag = false;
                for(int i = 0; i < n; i++) {
                    if(nums[i] == l) flag = true;
                }
                if(flag) {
                    lindex = k;
                    lmax = query2(0, N - 1, nums, scan);
                    if(lmax == -1) return;
                    break;
                }
            }

//            System.out.println("lindex:" + lindex + " lmax:" + lmax);

            StringBuilder sb = new StringBuilder();
            sb.append("!");
            for(int k = 0; k < K; k++) {
                if(k == lindex) {
                    sb.append(" " + lmax);
                } else {
                    sb.append(" " + max);
                }
            }
            System.out.println(sb);
            String res = scan.nextLine();
            if(!res.equals("Correct")) return;
            System.out.flush();
        }
    }

    //Fast IO class
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    private static void sort(double[] arr) {
        Double[] objArr = Arrays.stream(arr).boxed().toArray(Double[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }

    private static void sort(int[] arr) {
        Integer[] objArr = Arrays.stream(arr).boxed().toArray(Integer[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }

    private static void sort(long[] arr) {
        Long[] objArr = Arrays.stream(arr).boxed().toArray(Long[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }

    static class ModMath {
        private static final int DEFAULT_MOD = 1_000_000_007;
        private final long mod;

        public ModMath(long mod, boolean unsafe) {
        /*if (!unsafe && !IntMath.isPrime(mod)) {
            throw new RuntimeException("This class is designed for primes!");
        }*/
            this.mod = mod;
        }

        public ModMath(long mod) {
            this(mod, false);
        }

        public ModMath() {
            this(DEFAULT_MOD, true);
        }

        public long mod(long x) {
            x %= mod;
            return x < 0 ? x + mod : x;
        }

        public long inv(long x) {
            //return pow(x, mod - 2);
            return mod(LongEuclidSolver.solve(x, mod).x);
        }

        public Factorial getFactorial(int n) {
            return new Factorial(this, n);
        }

    }

    static class Factorial {
        private final ModMath mod;
        private final long[] natural;
        private final long[] reverse;

        public Factorial(ModMath mod, int max) {
            this.mod = mod;
            this.natural = new long[max];
            this.reverse = new long[max];
            natural[0] = 1;
            for (int i = 1; i < max; i++) {
                natural[i] = mod.mod(natural[i - 1] * i);
            }
            reverse[max - 1] = mod.inv(natural[max - 1]);
            for (int i = max - 1; i > 0; i--) {
                reverse[i - 1] = mod.mod(reverse[i] * i);
            }
        }

        public long fact(long x) {
            return natural[(int) x];
        }

        public long factinv(long x) {
            return reverse[(int) x];
        }

        public long npr(long n, long r) {
            return n < r ? 0 : mod.mod(fact(n) * factinv(n - r));
        }

        public long ncr(long n, long r) {
            return mod.mod(npr(n, r) * factinv(r));
        }

        public String toString() {
            return "Factorial{" +
                    "natural=" + Arrays.toString(natural) +
                    ", reverse=" + Arrays.toString(reverse) +
                    '}';
        }

    }

    static class LongEuclidSolver {
        private LongEuclidSolver() {
        }

        public static Vec3l solve(long a, long b) {
            LongEuclidSolver.ReferenceLong p = new LongEuclidSolver.ReferenceLong(), q = new LongEuclidSolver.ReferenceLong();
            long d = solve(a, b, p, q);
            return new Vec3l(p.val, q.val, d);
        }

        private static long solve(long a, long b, LongEuclidSolver.ReferenceLong p, LongEuclidSolver.ReferenceLong q) {
            if (b == 0) {
                p.val = 1;
                q.val = 0;
                return a;
            } else {
                long d = solve(b, a % b, q, p);
                q.val -= (a / b) * p.val;
                return d;
            }
        }

        private static class ReferenceLong {
            private long val;

        }

    }

    static class Vec3l implements Comparable<Vec3l> {
        public long x;
        public long y;
        public long z;

        public Vec3l(long x, long y, long z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Vec3i vec3i = (Vec3i) o;
            return x == vec3i.x &&
                    y == vec3i.y &&
                    z == vec3i.z;
        }

        public int hashCode() {
            return Objects.hash(x, y, z);
        }

        public String toString() {
            return "(" + x + ", " + y + ", " + z + ")";
        }

        public int compareTo(Vec3l o) {
            if (x == o.x) {
                if (y == o.y) {
                    return Long.compare(z, o.z);
                }
                return Long.compare(y, o.z);
            }
            return Long.compare(x, o.x);
        }

    }

    static class Vec3i implements Comparable<Vec3i> {
        public int x;
        public int y;
        public int z;

        public Vec3i(int x, int y, int z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Vec3i vec3i = (Vec3i) o;
            return x == vec3i.x &&
                    y == vec3i.y &&
                    z == vec3i.z;
        }

        public int hashCode() {
            return Objects.hash(x, y, z);
        }

        public String toString() {
            return "(" + x + ", " + y + ", " + z + ")";
        }

        public int compareTo(Vec3i o) {
            if (x == o.x) {
                if (y == o.y) {
                    return Integer.compare(z, o.z);
                }
                return Integer.compare(y, o.z);
            }
            return Integer.compare(x, o.x);
        }

    }
}