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:
/**
 * @author derrick20
 */
import java.io.*;
import java.util.*;

public class SpanningWithOneFixed {
    public static void main(String[] args) throws Exception {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);

        int N = sc.nextInt();
        int M = sc.nextInt();
        int D = sc.nextInt();

        HashSet<Integer>[] adjList = new HashSet[N];
        Arrays.setAll(adjList, i -> new HashSet<>());
        ArrayList<Integer> branches = new ArrayList<>();
        for (int i = 0; i < M; i++) {
            int u = sc.nextInt() - 1;
            int v = sc.nextInt() - 1;
            if (u == 0 || v == 0) {
                branches.add(Math.max(u, v));
            }
            else {
                adjList[u].add(v);
                adjList[v].add(u);
            }
        }

        boolean[] vis = new boolean[N];
        ArrayDeque<Edge> forced = new ArrayDeque<>();
        for (int adj : branches) {
            // bfs inside that group if not reached yet
            if (vis[adj]) continue;
            forced.add(new Edge(0, adj));
            ArrayDeque<Integer> q = new ArrayDeque<>();
            q.add(adj);
            vis[adj] = true;
            while (q.size() > 0) {
                int curr = q.pollFirst();
                for (int next : adjList[curr]) {
                    if (!vis[next]) {
                        vis[next] = true;
                        q.add(next);
                    }
                }
            }
        }

        if (forced.size() > D || branches.size() < D) {
            out.println("NO");
        }
        else {
            vis = new boolean[N];
            vis[0] = true;
            ArrayDeque<Edge> spanningTree = new ArrayDeque<>();
            ArrayDeque<Integer> starts = new ArrayDeque<>();
            for (Edge e : forced) {
                vis[e.v] = true;
                spanningTree.add(e);
                starts.add(e.v);
            }
            D -= forced.size();
            for (int adj : branches) {
                if (!vis[adj] && D > 0) {
                    vis[adj] = true;
                    spanningTree.add(new Edge(0, adj));
                    starts.add(adj);
                    D--;
                }
            }
            // It's not correct to only branch of from the "leaders" of each component,
            // since it's possible that some of the branches we've added have closed off parts
            // of the graph from being added to the tree. But, it must be true that at least one
            // of the branches we've selected can reach it. Otherwise, this wouldn't be a component!
            for (int curr : starts) {
                ArrayDeque<Integer> q = new ArrayDeque<>();
                q.add(curr);
                while (q.size() > 0) {
                    int top = q.pollFirst();
                    for (int adj : adjList[top]) {
                        if (!vis[adj]) {
                            vis[adj] = true;
                            spanningTree.add(new Edge(top, adj));
                            q.add(adj);
                        }
                    }
                }
            }
            out.println("YES");
            if (spanningTree.size() != N - 1) {
                System.out.println("Invalid tree");
            }
            for (Edge e : spanningTree) {
                out.println(e);
            }
        }

        out.close();
    }

    static class Edge {
        int u, v;
        public Edge(int uu, int vv) {
            u = uu; v = vv;
        }
        public String toString() {
            return (u + 1) + " " + (v + 1);
        }
    }

    static class FastScanner {
        private int BS = 1<<16;
        private char NC = (char)0;
        private byte[] buf = new byte[BS];
        private int bId = 0, size = 0;
        private char c = NC;
        private double cnt = 1;
        private BufferedInputStream in;

        public FastScanner() {
            in = new BufferedInputStream(System.in, BS);
        }

        public FastScanner(String s) {
            try {
                in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
            }
            catch (Exception e) {
                in = new BufferedInputStream(System.in, BS);
            }
        }

        private char getChar(){
            while(bId==size) {
                try {
                    size = in.read(buf);
                }catch(Exception e) {
                    return NC;
                }
                if(size==-1)return NC;
                bId=0;
            }
            return (char)buf[bId++];
        }

        public int nextInt() {
            return (int)nextLong();
        }

        public int[] nextInts(int N) {
            int[] res = new int[N];
            for (int i = 0; i < N; i++) {
                res[i] = (int) nextLong();
            }
            return res;
        }

        public long[] nextLongs(int N) {
            long[] res = new long[N];
            for (int i = 0; i < N; i++) {
                res[i] = nextLong();
            }
            return res;
        }

        public long nextLong() {
            cnt=1;
            boolean neg = false;
            if(c==NC)c=getChar();
            for(;(c<'0' || c>'9'); c = getChar()) {
                if(c=='-')neg=true;
            }
            long res = 0;
            for(; c>='0' && c <='9'; c=getChar()) {
                res = (res<<3)+(res<<1)+c-'0';
                cnt*=10;
            }
            return neg?-res:res;
        }

        public double nextDouble() {
            double cur = nextLong();
            return c!='.' ? cur:cur+nextLong()/cnt;
        }

        public String next() {
            StringBuilder res = new StringBuilder();
            while(c<=32)c=getChar();
            while(c>32) {
                res.append(c);
                c=getChar();
            }
            return res.toString();
        }

        public String nextLine() {
            StringBuilder res = new StringBuilder();
            while(c<=32)c=getChar();
            while(c!='\n') {
                res.append(c);
                c=getChar();
            }
            return res.toString();
        }

        public boolean hasNext() {
            if(c>32)return true;
            while(true) {
                c=getChar();
                if(c==NC)return false;
                else if(c>32)return true;
            }
        }
    }
}