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.*;
	import java.util.Map.Entry;
	 
	 
	 class Main {
		 static int mod =  (int) (Math.pow(10,9)+7);
//		 static int mod =  (int) 998244353;
		 static List<ArrayList<Integer>> list= new ArrayList<ArrayList<Integer>>();
		 public static void main(String[] args) {
	    	
	        Scanner sc = new Scanner(System.in);
	        int N = sc.nextInt();
	        int M = sc.nextInt();
	        int[] a = new int[M];
	        int[] b = new int[M];
	        for(int i=0;i<N;i++)list.add(new ArrayList<Integer>());
	        for (int i=0 ; i<M; i++) {
	            a[i] = Integer.parseInt(sc.next())-1;
	            b[i] = Integer.parseInt(sc.next())-1;
	        	list.get(a[i]).add(b[i]);
	        	list.get(b[i]).add(a[i]);
	        }
	        int[] visited = new int[N];
	        LinkedList<Integer> q= new LinkedList<Integer>();
	        q.add(0);
	        q.add(-1);
	        while(!q.isEmpty()) {
	        	int now = q.poll();
	        	int pre = q.poll();
//        		visited[now]=pre+1;
	        	for(int i=0;i<list.get(now).size();i++) {
	        		int next = list.get(now).get(i);
	        		if(next==pre)continue;
	        		if(visited[next]!=0)continue;
	        		q.add(next);
	        		q.add(now);
	        		visited[next]=now+1;
	        	}
	        }
	        System.out.println("Yes");
	        for(int i=1;i<N;i++) {
	        	System.out.println(visited[i]);
	        }
	       
	    }

	}