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 void main(String[] args) {
        Scanner scan =  new Scanner(System.in);
        int n = scan.nextInt();
        int m = scan.nextInt();
        ArrayList<Integer>[] list = new ArrayList[n];
        for(int i=0;i<n;i++){
            ArrayList<Integer> sublist =  new ArrayList<>();
            list[i] = sublist;
        }

        for(int i=0;i<m;i++){
            int u = scan.nextInt() - 1;
            int v = scan.nextInt() - 1;
						list[u].add(v);
						list[v].add(u);
        }

        Queue<Integer> queue = new ArrayDeque<>();

				queue.add(0);

				int[] visit =  new int[n];
				visit[0]=1;
				int[] bef =  new int[n];

        while(!queue.isEmpty()){
					int from = queue.poll();
						for (int i=0;i<list[from].size();i++){
							int lf = list[from].get(i);
							if ( visit[lf] == 0){
								bef[lf] = from;
								visit[lf] = 1;
								queue.add(lf);
							}
						}
				}
				
				System.out.println("Yes");
				for(int i=1;i<bef.length;i++){
					System.out.println(bef[i]+1);
				}

    }
}