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.util.*;
import java.io.*;
import static java.lang.Math.*;

/* spar5h */

public class cf4 implements Runnable {   
	
	static class Pair {
		
		int u, v;
		
		Pair(int u, int v) {
			this.u = u; this.v = v;
		}
	}
	
	static ArrayList<Integer>[] adj;
	static int[] col;
	
	static void join(int u, int v) {
		
		int big = col[u], small = col[v];
		
		if(adj[big].size() < adj[small].size()) {
			int temp = small;
			small = big;
			big = temp;
		}
		
		for(int x : adj[small]) { 
			adj[big].add(x);
			col[x] = big;
		}
		
		adj[small].clear();
	}
	
	public void run() {
			
		InputReader s = new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);
		
		int n = s.nextInt(), m = s.nextInt(), d = s.nextInt();
		
		ArrayList<Pair> edge = new ArrayList<Pair>();
		
		int[] deg = new int[n];
		
		for(int i = 0; i < m; i++) {
			int u = s.nextInt() - 1, v = s.nextInt() - 1;
			edge.add(new Pair(u, v));
			deg[u]++; deg[v]++;
		}
		
		adj = new ArrayList[n];
		col = new int[n];
		
		HashSet<Integer> hs = new HashSet<Integer>();
		HashSet<Integer> hsCol = new HashSet<Integer>();
		
		for(int i = 0; i < n; i++) {
			adj[i] = new ArrayList<Integer>();
			adj[i].add(i);
			col[i] = i;
		}	
		
		for(int i = 0; i < m; i++) {
			
			if(edge.get(i).u == 0) {
				hs.add(edge.get(i).v);
				hsCol.add(col[edge.get(i).v]);
			}
			if(edge.get(i).v == 0){
				hs.add(edge.get(i).u);
				hsCol.add(col[edge.get(i).u]);
			}	
		}		
		
		ArrayList<String> res = new ArrayList<String>();
		
		for(int i = 0; i < m; i++) {
			
			if(edge.get(i).u == 0 || edge.get(i).v == 0 || (hsCol.contains(col[edge.get(i).u]) &&  hsCol.contains(col[edge.get(i).v])))
				continue;
			
			if(col[edge.get(i).u] != col[edge.get(i).v]) {
				res.add((edge.get(i).u + 1) + " " + (edge.get(i).v + 1));
				
				int oldU = -1, oldV = -1; 
				
				if(hsCol.contains(col[edge.get(i).u])) 
					oldU = col[edge.get(i).u];
				
				if(hsCol.contains(col[edge.get(i).v]))
					oldV = col[edge.get(i).v];
				
				join(edge.get(i).u, edge.get(i).v);
				
				if(oldU != -1) {
					hsCol.remove(oldU);
					hsCol.add(col[edge.get(i).u]);
				}
				
				if(oldV != -1) {
					hsCol.remove(oldV);
					hsCol.add(col[edge.get(i).v]);
				}
			}
		}
		
		int k = hs.size();
		
		for(int i = 0; i < m && k > d; i++) {
			
			if(hsCol.contains(col[edge.get(i).u]) &&  hsCol.contains(col[edge.get(i).v])) {
			
				if(col[edge.get(i).u] != col[edge.get(i).v]) {
					
					res.add((edge.get(i).u + 1) + " " + (edge.get(i).v + 1));
					
					int oldU = -1, oldV = -1; 
					
					if(hsCol.contains(col[edge.get(i).u])) 
						oldU = col[edge.get(i).u];
					
					if(hsCol.contains(col[edge.get(i).v]))
						oldV = col[edge.get(i).v];
					
					join(edge.get(i).u, edge.get(i).v);
					
					if(oldU != -1) {
						hsCol.remove(oldU);
						hsCol.add(col[edge.get(i).u]);
					}
					
					if(oldV != -1) {
						hsCol.remove(oldV);
						hsCol.add(col[edge.get(i).v]);
					}
					
					k--;
				}
			}
		}
		
		for(int i = 0; i < m; i++) {
			
			if(edge.get(i).u != 0 && edge.get(i).v != 0)
				continue;
			
			if(col[edge.get(i).u] != col[edge.get(i).v]) {
				res.add((edge.get(i).u + 1) + " " + (edge.get(i).v + 1));
				join(edge.get(i).u, edge.get(i).v);
			}
		}
		
		if(res.size() == n - 1 && k == d) {
			
			w.println("YES");
			
			for(int i = 0; i < res.size(); i++)
				w.println(res.get(i));
			
		}
		else
			w.println("NO");
		
		w.close();
	}

	static class InputReader {
		
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
		
		public int read() {
			
			if (numChars==-1) 
				throw new InputMismatchException();
			
			if (curChar >= numChars) {
				
				curChar = 0;
				
				try {
					numChars = stream.read(buf);
				}
				catch (IOException e) {
					throw new InputMismatchException();
				}
				
				if(numChars <= 0)				
					return -1;
			}
			
			return buf[curChar++];
		}
		 
		public String nextLine() {
			
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
	        
			try {
	            str = br.readLine();
	        }
	        catch (IOException e) {
	            e.printStackTrace();
	        }
			
	        return str;
		}
		
		public int nextInt() {
		
			int c = read();
			
			while(isSpaceChar(c)) 
				c = read();
			
			int sgn = 1;
			
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			
			int res = 0;
			
			do {
				if(c<'0'||c>'9') 
					throw new InputMismatchException();
				
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c)); 
			
			return res * sgn;
		}
		
		public long nextLong() {
			
			int c = read();
			
			while (isSpaceChar(c))
				c = read();
			
			int sgn = 1;
			
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			
			long res = 0;
			
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				
				res *= 10;
				res += c - '0';
				c = read();
			}
			
			while (!isSpaceChar(c));
				return res * sgn;
		}
		
		public double nextDouble() {
			
			int c = read();
			
			while (isSpaceChar(c))
				c = read();
			
			int sgn = 1;
			
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			
			double res = 0;
			
			while (!isSpaceChar(c) && c != '.') {
				
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				
				res *= 10;
				res += c - '0';
				c = read();
			}
			
			if (c == '.') {
				
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) 
				{
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, nextInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			
			return res * sgn;
		}
		
		public String readString() {
			
			int c = read();
			
			while (isSpaceChar(c))
				c = read();
			
			StringBuilder res = new StringBuilder();
			
			do {
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isSpaceChar(c));
			
			return res.toString();
		}
	 
		public boolean isSpaceChar(int c) {
			
			if (filter != null)
				return filter.isSpaceChar(c);
			
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	 
		public String next() {
			return readString();
		}
		
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	
	}

	public static void main(String args[]) throws Exception {
		new Thread(null, new cf4(),"cf4",1<<26).start();
	}
}