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 static java.lang.Math.*;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class GuessTheMaximums {
    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(in.nextInt(), in, out);
        out.close();
    }
    static class TaskA {
        long mod = (long)(998244353);
        long fact[];
        int depth[];
        int parentTable[][];
        int degree[];
        ArrayList<Integer> leaves;
        int max = Integer.MIN_VALUE;
        int min = Integer.MAX_VALUE;
    	int r[] = new int[]{1 , -1 , 0 , 0};
    	int c[] = new int[]{0 , 0 , 1 , -1};
        public void solve(int testNumber, InputReader in, PrintWriter out) throws IOException {
            while(testNumber-->0){
                int n = in.nextInt();
                int k = in.nextInt();
                ArrayList<Integer> a[] = new ArrayList[k];
                for(int i=0;i<k;i++)
                	a[i] = new ArrayList<>();
                for(int i=0;i<k;i++){
                	int c = in.nextInt();
                	for(int j=0;j<c;j++)
                		a[i].add(in.nextInt());
                }
                
                System.out.print("? " + n + " ");
                for(int i=1;i<=n;i++)
                	System.out.print(i + " ");
                System.out.println();
                System.out.flush();
                
                int max = in.nextInt();
                int index = -1;
                int start = 1;
                int end = n;
                while(start!=end){
                	int mid = (start+end)/2;
                	
                	System.out.print("? " + (mid-start+1) + " ");
                	for(int i=start;i<=mid;i++)
                		System.out.print(i + " ");
                	System.out.println();
                	System.out.flush();

                	int value = in.nextInt();
                	if(value<max)
                		start = mid+1;
                	else
                		end = mid;
                }
                if(start == end)
                	index = start;
                int ans[] = new int[k];
                for(int i=0;i<k;i++){
                	boolean contains = false;
                	for(int j=0;j<a[i].size();j++)
                		if(a[i].get(j) == index)
                			contains = true;
                	if(!contains)
                		ans[i] = max;
                	else{
                		HashSet<Integer> s = new HashSet<>();
                		for(int j=1;j<=n;j++)
                			s.add(j);
                		for(int j=0;j<a[i].size();j++)
                			s.remove(a[i].get(j));
                		
                		System.out.print("? " + s.size() + " ");
                		for(int j:s)
                			System.out.print(j + " ");
                		System.out.println();
                		System.out.flush();

                		int x = in.nextInt();
                		ans[i] = x;
                	}
                }
                System.out.print("! ");
                for(int i=0;i<k;i++)
                	System.out.print(ans[i] + " ");
                System.out.println();
                System.out.flush();
                in.next();
                // if(in.next() != "Correct")
                // 	break;
            }
        }
        /*
3 4 1 2

1
4 4
1 2
1 1
1 4
1 3
        */

        public void dfs(int a[][] , int x , int y){
        	a[x][y] = 2;
        	for(int i=0;i<4;i++){
        		int row = x+r[i];
        		int col = y+c[i];
        		if(row<0 || col<0 || row == a.length || col == a[row].length || a[row][col] == 0 || a[row][col] == 2)
        			continue;
        		dfs(a , row , col);
        	}
        }

        public int distance(ArrayList<ArrayList<Integer>> a , int u , int v){
            return depth[u]+depth[v] - 2*depth[lca(a , u , v)];
        }

        // public void dfs(ArrayList<ArrayList<Integer>> a , int index , int parent){
        //     parentTable[index][0] = parent;
        //     depth[index] = depth[parent]+1;
            
        //     if(a.get(index).size()==1)
        //         leaves.add(index);

        //     for(int i=1;i<parentTable[index].length;i++)
        //         parentTable[index][i] = parentTable[parentTable[index][i-1]][i-1];
        //     for(int i=0;i<a.get(index).size();i++){
        //         if(a.get(index).get(i)==parent)
        //             continue;
        //         dfs(a , a.get(index).get(i) , index);
        //     }
        // }

        public int lca(ArrayList<ArrayList<Integer>> a , int u , int v){
            if(depth[v]<depth[u]){
                int x = u;
                u = v;
                v = x;
            }
            int diff = depth[v] - depth[u];
            for(int i=0;i<parentTable[v].length;i++){
                // checking whether the ith bit is set in the diff variable
                if(((diff>>i)&1) == 1)
                    v = parentTable[v][i];
            }
            if(v == u)
                return v;
            for(int i=parentTable[v].length-1;i>=0;i--){
                if(parentTable[u][i] != parentTable[v][i]){
                    v = parentTable[v][i];
                    u = parentTable[u][i];
                }
            }
            return parentTable[u][0];
        }

        // for the min max problems
        public void build(int lookup[][] , int arr[], int n) { 
            for (int i = 0; i < n; i++) 
                lookup[i][0] = arr[i]; 
            for (int j = 1; (1 << j) <= n; j++) { 
                for (int i = 0; (i + (1 << j) - 1) < n; i++) { 
                    if (lookup[i][j - 1] > lookup[i + (1 << (j - 1))][j - 1]) 
                        lookup[i][j] = lookup[i][j - 1]; 
                    else
                        lookup[i][j] = lookup[i + (1 << (j - 1))][j - 1]; 
                } 
            } 
        }
        public int query(int lookup[][] , int L, int R) { 
            int j = (int)(Math.log(R - L + 1)/Math.log(2)); 
            if (lookup[L][j] >= lookup[R - (1 << j) + 1][j]) 
                return lookup[L][j]; 
            else
                return lookup[R - (1 << j) + 1][j]; 
        }

        // for printing purposes
        public void print1d(int a[] , PrintWriter out){
            for(int i=0;i<a.length;i++)
                out.print(a[i] + " ");
            out.println();
        }
        public void print2d(int a[][] , PrintWriter out){
            for(int i=0;i<a.length;i++){
                for(int j=0;j<a[i].length;j++)
                    out.print(a[i][j] + " ");
                out.println();
            }
            out.println();
        }
        public void sieve(int a[]){
            a[0] = a[1] = 1;
            int i;
            for(i=2;i*i<=a.length;i++){
                if(a[i] != 0)
                    continue;
                a[i] = i;
                for(int k = (i)*(i);k<a.length;k+=i){
                    if(a[k] != 0)
                        continue;
                    a[k] = i;
                }
            }
        }
        public int [][] matrixExpo(int c[][] , int n){
            int a[][] = new int[c.length][c[0].length];
            int b[][] = new int[a.length][a[0].length];
            for(int i=0;i<c.length;i++)
                for(int j=0;j<c[0].length;j++)
                    a[i][j] = c[i][j];
            for(int i=0;i<a.length;i++)
                b[i][i] = 1;
            while(n!=1){
                if(n%2 == 1){
                    b = matrixMultiply(a , a);
                    n--;
                }
                a = matrixMultiply(a , a);
                n/=2;
            }
            return matrixMultiply(a , b);
        }
        public int [][] matrixMultiply(int a[][] , int b[][]){
            int r1 = a.length;
            int c1 = a[0].length;
            int c2 = b[0].length;
            int c[][] = new int[r1][c2];
            for(int i=0;i<r1;i++){
                for(int j=0;j<c2;j++){
                    for(int k=0;k<c1;k++)
                        c[i][j] += a[i][k]*b[k][j];
                }
            }
            return c;
        }
        public long nCrPFermet(int n , int r , long p){
            if(r==0)
                return 1l;
            // long fact[] = new long[n+1];
            // fact[0] = 1;
            // for(int i=1;i<=n;i++)
            //     fact[i] = (i*fact[i-1])%p;
            long modInverseR = pow(fact[r] , p-2 , p);
            long modInverseNR = pow(fact[n-r] , p-2 , p);
            long w = (((fact[n]*modInverseR)%p)*modInverseNR)%p;
            return w;
        }
        public long pow(long a, long b, long m) {
            a %= m;
            long res = 1;
            while (b > 0) {
                long x = b&1;
                if (x == 1)
                    res = res * a % m;
                a = a * a % m;
                b >>= 1;
            }
            return res;
        }
        public long pow(long a, long b) {
            long res = 1;
            while (b > 0) {
                long x = b&1;
                if (x == 1)
                    res = res * a;
                a = a * a;
                b >>= 1;
            }
            return res;
        }
        public void swap(int a[] , int p1 , int p2){
            int x = a[p1];
            a[p1] = a[p2];
            a[p2] = x;
        }
        public void sortedArrayToBST(TreeSet<Integer> a , int start, int end) { 
            if (start > end) {
                return;
            }
            int mid = (start + end) / 2;
            a.add(mid);
            sortedArrayToBST(a, start, mid - 1);
            sortedArrayToBST(a, mid + 1, end); 
        }
        class Combine{
            int value;
            int delete;
            Combine(int val , int delete){
                this.value = val;
                this.delete = delete;
            }
        }
        class Sort2 implements Comparator<Combine>{
            public int compare(Combine a , Combine b){
                if(a.value > b.value)
                    return 1;
                else if(a.value == b.value && a.delete>b.delete)
                    return 1;
                else if(a.value == b.value && a.delete == b.delete)
                    return 0;
                return -1;
            }
        }
        public int lowerLastBound(ArrayList<Integer> a , int x){
            int l = 0;
            int r = a.size()-1;
            if(a.get(l)>=x)
                return -1;
            if(a.get(r)<x)
                return r;
            int mid = -1;
            while(l<=r){
                mid = (l+r)/2;
                if(a.get(mid) == x && a.get(mid-1)<x)
                    return mid-1;
                else if(a.get(mid)>=x)
                    r = mid-1;
                else if(a.get(mid)<x && a.get(mid+1)>=x)
                    return mid;
                else if(a.get(mid)<x && a.get(mid+1)<x)
                    l = mid+1;
            }
            return mid;
        }
        public int upperFirstBound(ArrayList<Integer> a , Integer x){
            int l = 0;
            int r = a.size()-1;
            if(a.get(l)>x)
                return l;
            if(a.get(r)<=x)
                return r+1;
            int mid = -1;
            while(l<=r){
                mid = (l+r)/2;
                if(a.get(mid) == x && a.get(mid+1)>x)
                    return mid+1;
                else if(a.get(mid)<=x)
                    l = mid+1;
                else if(a.get(mid)>x && a.get(mid-1)<=x)
                    return mid;
                else if(a.get(mid)>x && a.get(mid-1)>x)
                    r = mid-1;
            }
            return mid;
        }
        public int lowerLastBound(int a[] , int x){
            int l = 0;
            int r = a.length-1;
            if(a[l]>=x)
                return -1;
            if(a[r]<x)
                return r;
            int mid = -1;
            while(l<=r){
                mid = (l+r)/2;
                if(a[mid] == x && a[mid-1]<x)
                    return mid-1;
                else if(a[mid]>=x)
                    r = mid-1;
                else if(a[mid]<x && a[mid+1]>=x)
                    return mid;
                else if(a[mid]<x && a[mid+1]<x)
                    l = mid+1;
            }
            return mid;
        }
        public int upperFirstBound(long a[] , long x){
            int l = 0;
            int r = a.length-1;
            if(a[l]>x)
                return l;
            if(a[r]<=x)
                return r+1;
            int mid = -1;
            while(l<=r){
                mid = (l+r)/2;
                if(a[mid] == x && a[mid+1]>x)
                    return mid+1;
                else if(a[mid]<=x)
                    l = mid+1;
                else if(a[mid]>x && a[mid-1]<=x)
                    return mid;
                else if(a[mid]>x && a[mid-1]>x)
                    r = mid-1;
            }
            return mid;
        }
        public long log(float number , int base){
            return (long) Math.ceil((Math.log(number) / Math.log(base)) + 1e-9);
        }
        public long gcd(long a , long b){
            if(a<b){
                long c = b;
                b = a;
                a = c;
            }
            while(b!=0){
                long c = a;
                a = b;
                b = c%a;
            }
            return a;
        }
        public long[] gcdEx(long p, long q) {
            if (q == 0)
                return new long[] { p, 1, 0 };
            long[] vals = gcdEx(q, p % q);
            long d = vals[0];
            long a = vals[2];
            long b = vals[1] - (p / q) * vals[2];
            // 0->gcd 1->xValue 2->yValue
            return new long[] { d, a, b };
        }
        public void sievePhi(int a[]){
            a[0] = 0;
            a[1] = 1;
            for(int i=2;i<a.length;i++)
                a[i] = i-1;
            for(int i=2;i<a.length;i++)
                for(int j = 2*i;j<a.length;j+=i)
                    a[j] -= a[i];
        }
        public void lcmSum(long a[]){
            int sievePhi[] = new int[(int)1e6 + 1];
            sievePhi(sievePhi);
            a[0] = 0;
            for(int i=1;i<a.length;i++)
                for(int j = i;j<a.length;j+=i)
                    a[j] += (long)i*sievePhi[i];
        }
        static class AVLTree{
            Node root;
            public AVLTree(){
                this.root = null;
            }
            public int height(Node n){
                return (n == null ? 0 : n.height);
            }
            public int getBalance(Node n){
                return (n == null ? 0 : height(n.left) - height(n.right));
            }
            public Node rotateRight(Node a){
                Node b = a.left;
                Node br = b.right;

                a.lSum -= b.lSum;
                a.lCount -= b.lCount;
                
                b.rSum += a.rSum;
                b.rCount += a.rCount;
                
                b.right = a;
                a.left = br;
                
                a.height = 1 + Math.max(height(a.left) , height(a.right));
                b.height = 1 + Math.max(height(b.left) , height(b.right));
                return b;
            }
            public Node rotateLeft(Node a){
                Node b = a.right;
                Node bl = b.left;
                
                a.rSum -= b.rSum;
                a.rCount -= b.rCount;
                
                b.lSum += a.lSum;
                b.lCount += a.lCount;
                
                b.left = a;
                a.right = bl;
                
                a.height = 1 + Math.max(height(a.left) , height(a.right));
                b.height = 1 + Math.max(height(b.left) , height(b.right));
                return b;
            }
            public Node insert(Node root , long value){
                if(root == null){
                    return new Node(value);
                }
                if(value<=root.value){
                    root.lCount++;
                    root.lSum += value;
                    root.left =  insert(root.left , value);
                }
                if(value>root.value){
                    root.rCount++;
                    root.rSum += value;
                    root.right = insert(root.right , value);
                }
                // updating the height of the root
                root.height = 1 + Math.max(height(root.left) , height(root.right));
                int balance = getBalance(root);

                //ll
                if(balance>1 && value<=root.left.value)
                    return rotateRight(root);
                //rr
                if(balance<-1 && value>root.right.value)
                    return rotateLeft(root);
                //lr
                if(balance>1 && value>root.left.value){
                    root.left = rotateLeft(root.left);
                    return rotateRight(root);
                }
                //rl
                if(balance<-1 && value<=root.right.value){
                    root.right = rotateRight(root.right);
                    return rotateLeft(root);
                }
                return root;
            }
            public void insertElement(long value){
                this.root = insert(root , value);
            }
            public int getElementLessThanK(long k){
                int count = 0;
                Node temp = root;
                while(temp!=null){
                    if(temp.value == k){
                        if(temp.left == null || temp.left.value<k){
                            count += temp.lCount;
                            return count-1;
                        }
                        else
                            temp = temp.left;
                    }
                    else if(temp.value>k){
                        temp = temp.left;
                    }
                    else{
                        count += temp.lCount;
                        temp = temp.right;
                    }
                }
                return count;
            }
            public void inorder(Node root , PrintWriter out){
                Node temp = root;
                if(temp!=null){
                    inorder(temp.left , out);
                    out.println(temp.value + " " + temp.lCount + " " + temp.rCount);
                    inorder(temp.right , out);
                }
            }
        }
        static class Node{
            long value;
            long lCount , rCount;
            long lSum , rSum;
            Node left , right;
            int height;
            public Node(long value){
                this.value = value;
                left = null;
                right = null;
                lCount = 1;
                rCount = 1;
                lSum = value;
                rSum = value;
                height = 1;
            }
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

    }
}