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.util.*;
import java.io.*;
public class Red {
    static FastScanner f;
    static PrintWriter pw = new PrintWriter(System.out);
    static long mod = 1000_000_007;
    static long oo = Long.MAX_VALUE;
    static int ooo = Integer.MAX_VALUE;
    static double eps = 1e-12;

    public static void solve()throws IOException {
        int n = f.ni(); int m = f.ni();
        ArrayList<Integer> adj[] = new ArrayList[n + 1];

        for (int i = 1; i <= n; ++i) adj[i] = new ArrayList<>();

        int deg[] = new int[n + 1];
        int ans = 0 , idx = -1;
        for (int i = 0; i < m; ++i) {
            int u = f.ni(); int v = f.ni();
            ++deg[u];
            ++deg[v];
            if (deg[u] > ans) {
                ans = deg[u];
                idx = u;
            }
            if (deg[v] > ans) {
                ans = deg[v];
                idx = v;
            }
            adj[u].add(v);
            adj[v].add(u);
        }

        Queue<Integer> q = new LinkedList<>();
        q.add(idx);
        boolean vis[] = new boolean[n + 1];

        while (q.size() > 0) {
            int s = q.poll();
            vis[s] = true;
            for (Integer node : adj[s]) {
                if (!vis[node]) {
                    pn(s + " " + node);
                    vis[node] = true;
                    q.add(node);
                }
            }
        }
    }    
    
    public static void main(String args[])throws IOException {
        go();
        boolean test_cases = false;
        int t = test_cases ? f.ni() : 1;
        while (t --> 0) solve();
        pw.flush();
        pw.close(); 
    }

    public static void go()throws IOException {
        if (System.getProperty("ONLINE_JUDGE") == null) {
            f = new FastScanner("");
        }
        else f = new FastScanner(System.in);
    }

    public static class FastScanner {
        StringTokenizer st;
        BufferedReader br;
 
        public FastScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public FastScanner(String str) {
            try {
                br = new BufferedReader(new FileReader("inp.txt"));
            }
            catch (Exception e) {
                e.printStackTrace();
            }
        }
 
        public String next()throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
 
        public int ni() throws IOException {return Integer.parseInt(next());}
 
        public long nl() throws IOException {return Long.parseLong(next());}
 
        public String nextLine() throws IOException {return br.readLine();}

        public double nd() throws IOException {return Double.parseDouble(next());}
    }

    public static long mul(long a , long b) {
        return ((a % mod) * (b % mod)) % mod;
    }

    public static void sort(int a[]) {
        ArrayList<Integer> x = new ArrayList<>();
        for (int i : a) x.add(i);
        Collections.sort(x);
        for (int i = 0; i < a.length; ++i) a[i] = x.get(i);
    }
    
    public static void sort(long a[]) {
        ArrayList<Long> x = new ArrayList<>();
        for (Long i : a) x.add(i);
        Collections.sort(x);
        for (int i = 0; i < a.length; ++i) a[i] = x.get(i);
    }

    public static void pn(Object o){pw.println(o);}
        
    public static void p(Object o){pw.print(o);}
        
    public static void pni(Object o){pw.println(o);pw.flush();}

    static int gcd(int x , int y) {
        if (y == 0) return Math.abs(x);
        return gcd(y , x % y);
    }
}