Problem: You are given an undirected unweighted connected graph consisting of n vertices and m edges. It is guaranteed that there are no self-loops or multiple edges in the given graph.

Your task is to choose at most ⌊n/2⌋ vertices in this graph so each unchosen vertex is adjacent (in other words, connected by an edge) to at least one of chosen vertices.

It is guaranteed that the answer exists. If there are multiple answers, you can print any.

You will be given multiple independent queries to answer.

Input

The first line contains a single integer t (1 ≤ t ≤ 2 ⋅ 10^5) — the number of queries.

Then t queries follow.

The first line of each query contains two integers n and m (2 ≤ n ≤ 2 ⋅ 10^5, n - 1 ≤ m ≤ min(2 ⋅ 10^5, (n(n-1))/(2))) — the number of vertices and the number of edges, respectively.

The following m lines denote edges: edge i is represented by a pair of integers v_i, u_i (1 ≤ v_i, u_i ≤ n, u_i ≠ v_i), which are the indices of vertices connected by the edge.

There are no self-loops or multiple edges in the given graph, i. e. for each pair (v_i, u_i) there are no other pairs (v_i, u_i) or (u_i, v_i) in the list of edges, and for each pair (v_i, u_i) the condition v_i ≠ u_i is satisfied. It is guaranteed that the given graph is connected.

It is guaranteed that ∑ m ≤ 2 ⋅ 10^5 over all queries.

Output

For each query print two lines.

In the first line print k (1 ≤ ⌊n/2⌋) — the number of chosen vertices.

In the second line print k distinct integers c_1, c_2, ..., c_k in any order, where c_i is the index of the i-th chosen vertex.

It is guaranteed that the answer exists. If there are multiple answers, you can print any.

Example

Input


2
4 6
1 2
1 3
1 4
2 3
2 4
3 4
6 8
2 5
5 4
4 3
4 1
1 3
2 3
2 6
5 6


Output


2
1 3
3
4 3 6

Note

In the first query any vertex or any pair of vertices will suffice.

<image>

Note that you don't have to minimize the number of chosen vertices. In the second query two vertices can be enough (vertices 2 and 4) but three is also ok.

<image>

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
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.Collections;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Main {
	static  ArrayList<Integer>adj[];
	static PrintWriter out=new PrintWriter(System.out);
	 public static int mod = 1000000007;

	static Boolean notmemo[][][];
	static int k;
	static long a[];
	static long b[];
	static int m;
	static char c[];
	static int trace[];
	public static void main(String[] args) throws Exception {
	Scanner sc=new Scanner(System.in);
	int n=sc.nextInt();
	int m=sc.nextInt();
	adj=new ArrayList[n];
	for (int i = 0; i < adj.length; i++) {
		adj[i]=new ArrayList<Integer>();
	}
	while(m-->0) {
		int u=sc.nextInt()-1;
		int v=sc.nextInt()-1;
		adj[u].add(v);
		adj[v].add(u);
	}
	int max=0;
	int idx=0;
	for (int i = 0; i < adj.length; i++) {
		if(adj[i].size()>max) {
			max=adj[i].size();
			idx=i;
		}
	}
	PriorityQueue<Integer> pq=new PriorityQueue<>((a,b)->(adj[b].size()-adj[a].size()));
	pq.add(idx);
	boolean vis[]=new boolean[n];
	HashSet<Integer> set=new HashSet<Integer>();
	Queue <Integer> q=new LinkedList<>();
	while(!pq.isEmpty()) {
		int cur=pq.poll();
		vis[cur]=true;
		set.add(cur);
		for(int v:adj[cur]) {
			if(!vis[v]) {
				q.add(cur);
				q.add(v);
				vis[v]=true;
				pq.add(v);
			}
		}
	}
	while(!q.isEmpty()) {
	System.out.println((q.poll()+1)+" "+(q.poll()+1));
	}
	
		
	
	
	
	out.flush();
	
	}
	static int teams=0;
static long mini[];
static char x[]= {'h','a','r','d'};
static long s[];
static ArrayList<Integer> l1=new ArrayList<>();
static long count=0;

static long dp(int i,int j) {
	
	if(i>=n) {
	return 0;
}
	if(j==x.length) {
		return INF; 
	}



if(memo[i][j]!=-1) {
	return memo[i][j];
}
long ans=INF;
if(c[i]==x[j]) {
ans=Math.min(ans, dp(i+1, j)+b[i]);
ans=Math.min(ans, dp(i+1,j+1));
}
else {
	ans=Math.min(ans, dp(i+1,j));	
}


return memo[i][j]=ans;

}



private static int bs(int i) {
	int high=n-1;
	int low=i;
	int ans=-1;
	int count=1;
	while(high>=low) {
	int	mid=(high+low)>>1;
	if(a[mid]-a[i]<=5) {
		ans=mid;
		low=mid+1;
		count=mid-i+1;
	}
	else {
		high=mid-1;
		
	}
	}
	return count;
	
	
}



/**private static void trace(int i, int time) {
if(i==n) 
	return;


long ans=dp(i,time);
if(time+a[i].t<a[i].burn&&(ans==dp(i+1,time+a[i].t)+a[i].cost)) {
	
	trace(i+1, time+a[i].t);
    
	l1.add(a[i].idx);
    return;
}
    trace(i+1,time);

}**/



	static class incpair implements Comparable<incpair>
{
	int a; long b;
	int idx;
	incpair(int a, long dirg,int i) {this.a = a;	b = dirg; idx=i; }
	
	public int compareTo(incpair e){ return (int) (b - e.b);	}
}
	static class decpair implements Comparable<decpair>
{
	int a; long b;int idx;
	
	decpair(int a, long dirg,int i) {this.a = a;	b = dirg; idx=i;}
	
	public int compareTo(decpair e){ return (int) (e.b- b);	}
}

	
	
	
	
	
	


	static long allpowers[];
	static class Quad implements Comparable<Quad>{
		int u;
		int v;
		char state;
		int turns;
		public Quad(int i, int j, char c, int k) {
		u=i;
		v=j;
		state=c;
		turns=k;
		}
		public int compareTo(Quad e){ return (int) (turns - e.turns);	}
		
	}
	static long dirg[][];
	static Edge[] driver;
	
	static int n;
		static class Edge implements Comparable<Edge>
	{
		int node; long cost;
		
		Edge(int a, long dirg) { node = a;	cost = dirg; }
		
		public int compareTo(Edge e){ return (int) (cost - e.cost);	}
	}

	



	  static long manhatandistance(long x,long x2,long y,long y2) {
		  return  Math.abs(x-x2)+Math.abs(y-y2);
	  }
	  static long fib[];
	  static long fib(int n) {
		  if(n==1||n==0) {
			  return 1;
		  }
		  if(fib[n]!=-1) {
			  return fib[n];
		  }
		  else 
			  return  fib[n]=  ((fib(n-2)%mod+fib(n-1)%mod)%mod);
	  }
	  static class Pair implements Comparable<Pair>{
		  long val;
		  int idx;
		  Pair(int a, long b){
			  idx=a;
			  val=b;
		  }
		public int compareTo(Pair p) {
		
			return (int) (this.val-p.val);
		}
		  
		  
	
		
		
	}
	static long[][] comb;		
	static long nCr1(int n , int k)
	{
		if(n < k)
			return 0;
		if(k == 0 || k == n)
			return 1;
		if(comb[n][k] != -1)
			return comb[n][k];
		if(n - k < k)
			return comb[n][k] = nCr1(n, n - k);
		return comb[n][k] = (nCr1(n - 1, k - 1) + nCr1(n - 1, k))%mod;
	}
	
	
static  class Triple implements Comparable<Triple>{

int t;
int burn;
		int cost;
		int idx;
		public Triple(int a,int b,int l,int i) {
			t=a;
			burn=b;
			cost=l;
			idx=i;
		}
		@Override
		public int compareTo(Triple o) {
			return Long.compare( burn,o.burn);	
		}
		
	}
	
	static TreeSet<Long> primeFactors(long N)		// O(sqrt(N) / ln sqrt(N))
	{
		TreeSet<Long> factors = new TreeSet<Long>();		//take abs(N) in case of -ve integers
		int idx = 0, p = primes.get(idx);

		while(p * p <= N)
		{
			while(N % p == 0) { factors.add((long) p); N /= p; }
			if(primes.size()>idx+1)
			p = primes.get(++idx);
			else
				break;
		}

		if(N != 1)						// last prime factor may be > sqrt(N)
			factors.add(N);				// for integers whose largest prime factor has a power of 1
		return factors;
	}
	
	static boolean visited[];
	/**static int bfs(int s)
	{
		Queue<Integer> q = new LinkedList<Integer>();
		q.add(s);
		int count=0;
		int maxcost=0;
		int dist[]=new int[n];
		dist[s]=0;
		while(!q.isEmpty())
		{
			
			int u = q.remove();
			if(dist[u]==k) {
				break;
			}
			for(Pair v: adj[u])
			{	
				maxcost=Math.max(maxcost, v.cost);
			
			
			
			if(!visited[v.v])	{
				
				visited[v.v]=true;
				q.add(v.v);
				dist[v.v]=dist[u]+1;
				maxcost=Math.max(maxcost, v.cost);
			}
			}	
			
		}
		return maxcost;
	}**/
	public static boolean FindAllElements(int n, int k) {
	 int sum = k;  
     int[] A = new int[k];  
      Arrays.fill(A, 0, k, 1);  
        
      for (int i = k - 1; i >= 0; --i) {  
      
           while (sum + A[i] <= n) {  
      
              sum += A[i];  
              A[i] *= 2;  
          }  
      }  
      if(sum==n) {
      	return true;
      }
      else
    	return false; 
	}
	
	static long[][] memo;

	
	static boolean vis2[][];
	
	static class SegmentTree {		// 1-based DS, OOP
		
		int N; 			//the number of elements in the array as a power of 2 (i.e. after padding)
		int[] array, sTree, lazy;
		
		SegmentTree(int[] in)		
		{
			array = in; N = in.length - 1;
			sTree = new int[N<<1];		//no. of nodes = 2*N - 1, we add one to cross out index zero
			lazy = new int[N<<1];
			build(1,1,N);
		}
		
		void build(int node, int b, int e)	// O(n)
		{
			if(b == e)					
				sTree[node] = array[b];
			else						
			{
				int mid = b + e >> 1;
				build(node<<1,b,mid);
				build(node<<1|1,mid+1,e);
				sTree[node] = sTree[node<<1]+sTree[node<<1|1];
			}
		}
		
		
		void update_point(int index, int val)			// O(log n)
		{
			index += N - 1;				
			sTree[index] += val;			
			while(index>1)				
			{
				index >>= 1;
				sTree[index] = sTree[index<<1] + sTree[index<<1|1];		
			}
		}
		
		
		void update_range(int i, int j, int val)		// O(log n) 
		{
			update_range(1,1,N,i,j,val);
		}
		
		void update_range(int node, int b, int e, int i, int j, int val)
		{
			if(i > e || j < b)		
				return;
			if(b >= i && e <= j)		
			{
				sTree[node] += (e-b+1)*val;			
				lazy[node] += val;				
			}							
			else		
			{
				int mid = b + e >> 1;
				propagate(node, b, mid, e);
				update_range(node<<1,b,mid,i,j,val);
				update_range(node<<1|1,mid+1,e,i,j,val);
				sTree[node] = sTree[node<<1] + sTree[node<<1|1];		
			}
			
		}
		void propagate(int node, int b, int mid, int e)		
		{
			lazy[node<<1] += lazy[node];
			lazy[node<<1|1] += lazy[node];
			sTree[node<<1] += (mid-b+1)*lazy[node];		
			sTree[node<<1|1] += (e-mid)*lazy[node];		
			lazy[node] = 0;
		}
		
		int query(int i, int j)
		{
			return query(1,1,N,i,j);
		}
		
		int query(int node, int b, int e, int i, int j)	// O(log n)
		{
			if(i>e || j <b)
				return 0;		
			if(b>= i && e <= j)
				return sTree[node];
			int mid = b + e >> 1;
			propagate(node, b, mid, e);
			int q1 = query(node<<1,b,mid,i,j);
			int q2 = query(node<<1|1,mid+1,e,i,j);
			return q1 + q2;	
					
		}
	
	}
	static boolean f2=false;
	static long[][] matMul(long[][] a2, long[][] b, int p, int q, int r)	//C(p x r) = A(p x q) x (q x r) -- O(p x q x r)
	{
		long[][] C = new long[p][r];
		for(int i = 0; i < p; ++i) {
			for(int j = 0; j < r; ++j) {
				for(int k = 0; k < q; ++k) {
					C[i][j] = (C[i][j]+(a2[i][k]%mod * b[k][j]%mod))%mod;
		 C[i][j]%=mod;
				}
		
			}
		}
		return C;
	}
		
	
	
		
		
		
		

		
	
	static ArrayList<Pair> a1[];
	static int memo1[];
	
	static boolean vis[];
	static TreeSet<Integer> set=new TreeSet<Integer>();
	
	static long modPow(long ways, long count, long mod)	// O(log e)
	{
		ways %= mod;
		long res = 1;
		while(count > 0)
		{
			if((count & 1) == 1)
				res = (res * ways) % mod;
			ways = (ways * ways) % mod;
			count >>= 1;
		}
		return res%mod;
	}
	
	
	

	static long gcd(long ans,long b) {
		if(b==0) {
			return ans;
		}
		return gcd(b,ans%b);
	}
	static int[] isComposite;
	static int[] valid;
	
	static ArrayList<Integer> primes;
	static ArrayList<Integer> l;
	static void sieve(int N)	// O(N log log N) 
	{
		isComposite = new int[N+1];					
		isComposite[0] = isComposite[1] = 1;			// 0 indicates a prime number
		primes = new ArrayList<Integer>();
		l=new ArrayList<>();
		valid=new int[N+1];
		for (int i = 2; i <= N; ++i) 					//can loop till i*i <= N if primes array is not needed O(N log log sqrt(N)) 
			if (isComposite[i] == 0) 					//can loop in 2 and odd integers for slightly better performance
			{
				primes.add(i);
				l.add(i);
				valid[i]=1;
				
				for (int j = i*2; j <=N; j +=i) {	// j = i * 2 will not affect performance too much, may alter in modified sieve
						isComposite[j] = 1;
						
						
						
				      
					}
			}
		
		for(int i=0 ; i<primes.size() ; i++) {
			for(int j:primes) {
				if(primes.get(i)*j>N) {
					break;
				}
				valid[primes.get(i)*j]=1;
			}
		}
	}
	
	public static long[] schuffle(long[] a2) {
		for (int i = 0; i < a2.length; i++) {
			int x=(int)(Math.random()*a2.length);
		long temp=a2[x];
		a2[x]=a2[i];
		a2[i]=temp;
		}
		return a2;
	}
		static int V;
	static long INF=(long) 1E16;
		
		static class Edge2 
		{
			int node;
		long cost;
			long next;
			Edge2(int a, int c,Long long1) { node = a;	cost = long1; next=c;}
			
		}
static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}	
}