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:
import java.util.*;

public class Main{
    
    public static final int MOD = (int)1e9+7;
    
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        
        int n = Integer.parseInt(sc.next());
        int m = Integer.parseInt(sc.next());
        
        ArrayList<Integer>[] graph = new ArrayList[n];
        
        for(int i=0; i<n; i++){
            graph[i] = new ArrayList<>();
        }
        
        for(int i=0; i<m; i++){
            int a = Integer.parseInt(sc.next())-1;
            int b = Integer.parseInt(sc.next())-1;
            graph[a].add(b);
            graph[b].add(a);
        }
        
        int[] dist = new int[n];
        Arrays.fill(dist, (int)1e7);
        dist[0] = 0;
        ArrayDeque<Integer> q = new ArrayDeque<>();
        q.addLast(0);
        boolean[] used = new boolean[n];
        used[0] = true;
        int[] ans = new int[n];
        while(q.size()!=0){
            int now = q.pollFirst();
            for(int next : graph[now]){
                if(dist[now]+1 < dist[next]){
                    q.add(next);
                    dist[next] = dist[now]+1;
                    used[next] = true;
                    ans[next] = now+1;
                }
            }
        }
        
        System.out.println("Yes");
        for(int i=1; i<n; i++){
            System.out.println(ans[i]);
        }
        
    }
    
}