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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.StringTokenizer;



public class COVID {

	static ArrayList<Integer>[] adjList;






	static int[] fac;
	static int mod=998244353;
	static int pow(int b,long e) {
		int ans=1;
		while(e>0) {
			if((e&1)==1)
				ans=(int)((ans*1l*b));
			e>>=1;
			b=(int)((b*1l*b));
		}
		return ans;
	}

	static int powmod(int b,long e, int mod) {
		int ans=1;
		b%=mod;
		while(e>0) {
			if((e&1)==1)
				ans=(int)((ans*1l*b)%mod);
			e>>=1;
			b=(int)((b*1l*b)%mod);
		}
		return ans;
	}

	static int oneUnqiue(int[] arr) {
		int one=0;int two=0;
		for(int i=0;i<arr.length;i++) {
			two|=(one&arr[i]);
			one^=arr[i];
			int turnOff=~(one&two);
			two&=turnOff;
			one&=turnOff;

		}
		return one;
	}




	public static long check(long a, long k)
	{
		if(k==1)return a;
		long tmp=a;
		int min=10;
		int max=-1;
		while(tmp!=0) {
			int dig=(int)(a%10);
			min=Math.min(dig, min);
			max=Math.max(dig, max);
			tmp/=10;
		}
		return check(a+min*max,k-1);
	}
	ArrayList<Pair> arr;
	static int idx;

	public static boolean moreThanOne(char[] a, char[] b) {
		int c=0;
		for(int i=0;i<a.length;i++)
			if(a[i]!=b[i]) {
				c++;
				if(c>1)return true;
			}
		return false;
	}
	static int[][] grid;

	static int n,m,a,b;
	static int[] col;

	static Scanner sc;
	static PrintWriter pw;
	static int[] cost,pre,pos;
	public static void main(String[] args) throws Exception {
				sc = new Scanner(System.in);
				 int t=sc.nextInt();
				while(t-->0) {
					int n=sc.nextInt();
					int k=sc.nextInt();
					HashSet<Integer>[] S=new HashSet[k];
					for(int i=0;i<k;i++) {
						int c=sc.nextInt();
						S[i]=new HashSet<>();
						for(int j=0;j<c;j++)
							S[i].add(sc.nextInt());
					}
				
					int max=query(n, 1, n);
					if(max==-1)return;
					int lo=1;
					int hi=n;
					while(lo<hi) {
						int mid=lo+hi>>1;
						int q=query(mid-lo+1, lo, mid);
						if(q==-1)return;
						if(q==max) {
							hi=mid;
						}else {
							lo=mid+1;
						}
					}
					HashSet<Integer> set=new HashSet<>();
					ArrayList<Integer> list=new ArrayList<>();
					int idx=-1;
					for(int i=0;i<k;i++) {
						if(S[i].contains(lo)) {
							set=S[i];
							idx=i;
							break;
						}
					}
					for(int i=1;i<=n;i++) {
						if(!set.contains(i))
						list.add(i);
					}
					StringBuilder sb=new StringBuilder();
					
				sb.append("? "+list.size());
					for(int i=0;i<list.size();i++) {
						sb.append(" "+list.get(i));
					}
					System.out.println(sb.toString());
					
					
					int rep=sc.nextInt();
					if(rep==-1)return;
					sb=new StringBuilder();
					sb.append("!");
					for(int i=0;i<k;i++) {
						if(i==idx)
							sb.append(" "+rep);
						else {
							sb.append(" "+max);
						}
					}
					System.out.println(sb.toString());
					
					String s=sc.next();
					if(!s.equals("Correct"))break;
				}

	}
	static long INF=(long)(1e16);
	static long[] memo;

	public static void  sum(int n) {
		vis[n]=true;
		for(int v:adjList[n])
			if(!vis[v])
			{
				sum(v);
				pre[n]+=pre[v];
				pos[n]+=pos[v];
			}
	}
	public static int query(int size,int from , int to) throws IOException {
		StringBuilder sb=new StringBuilder();
		sb.append("? "+size);
		for(int i=from;i<=to;i++) {
			sb.append(" "+i);
		}
		System.out.println(sb.toString());
		return sc.nextInt();
	}
	static int[] deg;
	static boolean[]vis;
	static int  dfs(int n) {
		if(vis[n])return 0;
		vis[n]=true;
		int ans=deg[n];
		for(int v:adjList[n])
			if(!vis[v])
				ans+=dfs(v);
		return ans;
	}

	static int bs(int[] a, int val) {
		int l=0;
		int h=a.length-1;
		while(l<=h) {
			int mid=(l+h+1)>>1;
		if(a[mid]>=val)
			h=mid-1;
		else
			l=mid+1;
		}
		return h+1;
	}


	static boolean[] isPrime;
	static ArrayList<Integer> primes;
	public static void sieve(int N) {// O( n log( log n ) )
		isPrime= new boolean[N+1];//u can save half the memory by neglecting all even numbers since they aren't primes
		primes= new ArrayList<>(N);
		Arrays.fill(isPrime, true);
		isPrime[0]=isPrime[1]=false;
		for(int i=2;i*i<=N;i++) {
			if(isPrime[i]) {
				for(int j=i*i;j<=N;j+=i) {
					isPrime[j]=false;
				}
			}
		}
		for(int i=2;i<=N;i++) {
			if(isPrime[i])primes.add(i);
		}
	}

	static long gcd(long a, long b) {
		return (b==0)?a:gcd(b,a%b);
	}
	static long lcm(long a, long b) {
		return a/gcd(a,b)*b;
	}
	public static int log(int n , int base) {
		int ans=0;
		while(n+1>base) {
			ans++;
			n/=base;
		}
		return ans;
	}
	static long square(long l) {
		return l*l;
	}






	static class Pair implements Comparable<Pair>{
		int  x;int y;

		public Pair(int a,int b) {
			this.x=a;y=b;
		}



		public int compareTo(Pair o) {
			return (x==o.x)?((y>o.y)?1:(y==o.y)?0:-1):((x>o.x)?1:-1);
		}


		@Override

		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + x;
			result = prime * result + y;
			return result;
		}


		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Pair other = (Pair) obj;
			if (x != other.x)
				return false;
			if (y != other.y)
				return false;
			return true;
		}

	}





	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}
		public Scanner(String s) throws FileNotFoundException{	br = new BufferedReader(new FileReader(s));}

		public long[] nextLongArr(int n) throws IOException {
			long[] arr=new long[n];
			for(int i=0;i<n;i++)
				arr[i]=nextLong();
			return arr;
		}
		public int[] nextIntArr(int n) throws IOException {
			int[] arr=new int[n];
			for(int i=0;i<n;i++)
				arr[i]=nextInt();
			return arr;
		}
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine()," ,");
			return st.nextToken();
		}

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

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

		public String nextLine() throws IOException {
			return br.readLine();
		}


		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++) {
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
				if (sb.length() == 18) {
					res += Long.parseLong(sb.toString()) / f;
					sb = new StringBuilder("0");
				}
			}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}

	public static void shuffle(int[] a) {
		int n = a.length;
		for (int i = 0; i < n; i++) {
			int r = i + (int) (Math.random() * (n - i));
			int tmp = a[i];
			a[i] = a[r];
			a[r] = tmp;
		}
	}
}