Problem: There is a cave.

The cave has N rooms and M passages. The rooms are numbered 1 to N, and the passages are numbered 1 to M. Passage i connects Room A_i and Room B_i bidirectionally. One can travel between any two rooms by traversing passages. Room 1 is a special room with an entrance from the outside.

It is dark in the cave, so we have decided to place a signpost in each room except Room 1. The signpost in each room will point to one of the rooms directly connected to that room with a passage.

Since it is dangerous in the cave, our objective is to satisfy the condition below for each room except Room 1.

* If you start in that room and repeatedly move to the room indicated by the signpost in the room you are in, you will reach Room 1 after traversing the minimum number of passages possible.



Determine whether there is a way to place signposts satisfying our objective, and print one such way if it exists.

Constraints

* All values in input are integers.
* 2 \leq N \leq 10^5
* 1 \leq M \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq N\ (1 \leq i \leq M)
* A_i \neq B_i\ (1 \leq i \leq M)
* One can travel between any two rooms by traversing passages.

Input

Input is given from Standard Input in the following format:


N M
A_1 B_1
:
A_M B_M


Output

If there is no way to place signposts satisfying the objective, print `No`.

Otherwise, print N lines. The first line should contain `Yes`, and the i-th line (2 \leq i \leq N) should contain the integer representing the room indicated by the signpost in Room i.

Examples

Input

4 4
1 2
2 3
3 4
4 2


Output

Yes
1
2
2


Input

6 9
3 4
6 1
2 4
5 3
4 6
1 5
6 2
4 5
5 6


Output

Yes
6
5
5
1
1

Solution (in JAVA):

Solution:
//20200517 D
import java.util.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt();
		int m=sc.nextInt();
		List[] e=new List[n];
		for(int i=0;i<n;i++){
			e[i]=new ArrayList<Integer>();
		}
		int[] q=new int [n];
      	int a;
      	int b;
		for(int i=0;i<m;i++){
			a=sc.nextInt();
			b=sc.nextInt();
          	e[a-1].add(b);
          	e[b-1].add(a);
        }
      	int h=0; 
        int f=0;
        q[0]=1;
      	boolean[] v=new boolean[n];
      	v[0]=true;
      	List<Integer> t;
      	int s;
      	int[] ans=new int[n-1];
		while(h<n){
           // System.out.println(h);
 			t=e[q[h]-1];
			for(int i=0;i<t.size();i++){
              	s=t.get(i);
            	if(!v[s-1]){
                  f++;
                	q[f]=s;
                  	v[s-1]=true;
                  	ans[s-2]=q[h];
                }
            }
          	h++;
        } 
        if(true){
			System.out.println("Yes");
          for(int i=0;i<n-1;i++){
			System.out.println(ans[i]);
		  }
		}else{
			System.out.println("No");
		}
    }
}