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 find any spanning tree of this graph such that the degree of the first vertex (vertex with label 1 on it) is equal to D (or say that there are no such spanning trees). Recall that the degree of a vertex is the number of edges incident to it.

Input

The first line contains three integers n, m and D (2 ≤ n ≤ 2 ⋅ 10^5, n - 1 ≤ m ≤ min(2 ⋅ 10^5, (n(n-1))/(2)), 1 ≤ D < n) — the number of vertices, the number of edges and required degree of the first vertex, 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 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.

Output

If there is no spanning tree satisfying the condition from the problem statement, print "NO" in the first line.

Otherwise print "YES" in the first line and then print n-1 lines describing the edges of a spanning tree such that the degree of the first vertex (vertex with label 1 on it) is equal to D. Make sure that the edges of the printed spanning tree form some subset of the input edges (order doesn't matter and edge (v, u) is considered the same as the edge (u, v)).

If there are multiple possible answers, print any of them.

Examples

Input


4 5 1
1 2
1 3
1 4
2 3
3 4


Output


YES
2 1
2 3
3 4


Input


4 5 3
1 2
1 3
1 4
2 3
3 4


Output


YES
1 2
1 3
4 1


Input


4 4 3
1 2
1 4
2 3
3 4


Output


NO

Note

The picture corresponding to the first and second examples: <image>

The picture corresponding to the third example: <image>

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.awt.Point;

public class CF_1133F2 {
    static final String name = "CF_1133F2";
    static final boolean test = new File(name + ".in").exists();

    static ArrayList<ArrayList<Integer>> adj;
    public static void main(String args[]) throws Exception {
        BufferedScanner in = new BufferedScanner(test ? new FileInputStream(name + ".in") : System.in);
        BufferedPrinter out = new BufferedPrinter(test ? new FileOutputStream(name + ".out") : System.out);

        int n = in.nextInt(), m = in.nextInt(), d = in.nextInt();
        adj = get2D(n);

        for(int i = 0; i < m; i++){
            int u = in.nextInt() - 1, v = in.nextInt() - 1;

            adj.get(u).add(v);
            adj.get(v).add(u);
        }

        ArrayList<Integer> sets = new ArrayList<>();
        vis = new boolean[n];
        vis[0] = true;
        for(Integer v: adj.get(0)){
            if(!vis[v]) {
                sets.add(v);
                dfs(v, false);
            }
        }

        if(adj.get(0).size() < d || sets.size() > d) out.println("NO");
        else {
            out.println("YES");

            vis = new boolean[n];
            vis[0] = true;
            for(int i = 0; i < sets.size(); i++){
                vis[sets.get(i)] = true;
                ed.add(new Point(0, sets.get(i)));
            }

            for(int i = 0; sets.size() < d; i++){
                int nxt = adj.get(0).get(i);
                if(!vis[nxt]){
                    vis[nxt] = true;
                    ed.add(new Point(0, nxt));

                    sets.add(nxt);
                }
            }

            for(Integer v: sets) dfs(v, true);

            for(Point p: ed){
                out.println((p.x + 1) + " " + (p.y + 1));
            }
        }

        out.close();
        in.close();
    }
    static ArrayList<Point> ed = new ArrayList<>();
    static boolean[] vis;
    static void dfs(int curr, boolean add){
        for(Integer v: adj.get(curr)){
            if(!vis[v]) {
                vis[v] = true;
                if(add) ed.add(new Point(curr, v));

                dfs(v, add);
            }
        }
    }

    /**
     * My template below. FastIO and utility functions.
     * Minimized with https://codebeautify.org/javaviewer.
     */

    // @formatter:off
    static<T>ArrayList<ArrayList<T>>get2D(int n){ArrayList<ArrayList<T>>ret=new ArrayList<>();for(int i=0;i<n;i++)ret.add(new ArrayList<>());return ret;}
    static void force(boolean condition){if(!condition)throw new IllegalStateException();}
    static void debug(Object obj){if(obj instanceof long[][]){for(long[]a:(long[][])obj)System.out.println(Arrays.toString(a));}
    else if(obj instanceof int[][]){for(int[]a:(int[][])obj)System.out.println(Arrays.toString(a));}
    else if(obj instanceof char[][]){for(char[]a:(char[][])obj)System.out.println(Arrays.toString(a));}
    else if(obj instanceof boolean[][]){for(boolean[]a:(boolean[][])obj)System.out.println(Arrays.toString(a));}
    else if(obj instanceof long[]){System.out.println(Arrays.toString((long[])obj));}
    else if(obj instanceof int[]){System.out.println(Arrays.toString((int[])obj));}
    else if(obj instanceof char[]){System.out.println(Arrays.toString((char[])obj));}
    else if(obj instanceof boolean[]){System.out.println(Arrays.toString((boolean[])obj));}
    else{System.out.println(obj);}}
    static class BufferedPrinter{PrintWriter out;BufferedPrinter(OutputStream out){this(new OutputStreamWriter(out));}
    BufferedPrinter(Writer out){this.out=new PrintWriter(new BufferedWriter(out));}
    void print(Object...os){for(int i=0;i<os.length;i++){if(i!=0)out.print(' ');out.print(os[i]);}}
    void println(Object...os){print(os);out.println();}
    void close(){out.close();}
    void flush(){out.flush();}}
    static class BufferedScanner{private final InputStream in;private final byte[]buf=new byte[1<<13];int pos,count;BufferedScanner(InputStream in)throws IOException{this.in=in;}
    long nextLong()throws IOException{return Long.parseLong(next());}
    int[]nextN(int n)throws IOException{int[]ret=new int[n];for(int i=0;i<n;i++)ret[i]=this.nextInt();return ret;}
    long[]nextNL(int n)throws IOException{long[]ret=new long[n];for(int i=0;i<n;i++)ret[i]=this.nextLong();return ret;}
    private int read(){if(count==-1)err();try{if(pos>=count){pos=0;count=in.read(buf);if(count<=0)return-1;}}catch(IOException e){err();}
    return buf[pos++];}
    private static boolean isSpace(int c){return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;}
    private int readSkipSpace(){int ret;do{ret=read();}while(isSpace(ret));return ret;}
    int nextInt(){int sign=1;int c=readSkipSpace();if(c=='-'){sign=-1;c=read();}
    int ret=0;do{if(c<'0'||c>'9')err();ret=ret*10+c-'0';c=read();}while(!isSpace(c));return sign*ret;}
    String next(){StringBuilder sb=new StringBuilder();int c=readSkipSpace();do{sb.append((char)c);c=read();}while(!isSpace(c));return sb.toString();}
    private void err(){throw new InputMismatchException();}
    void close()throws IOException{in.close();}}
    // @formatter:on
}