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.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
        Scanner input = new Scanner(System.in);

        while (input.hasNext()) {
        	int N = input.nextInt();
        	int M = input.nextInt();
			ArrayList<ArrayList<Integer>> g = new ArrayList<ArrayList<Integer>>(N + 1);
        	
        	for (int i = 0; i < N + 1; ++i) {
        		g.add(new ArrayList<Integer>());
        	}
        	
        	for (int i = 0; i < M; ++i){
        		int A = input.nextInt();
        		int B = input.nextInt();
        		
        		g.get(A).add(B);
        		g.get(B).add(A);
        	}
        	
        	int[] nextRoom = new int[N + 1];
        	Arrays.fill(nextRoom, -1);
        	Queue<Integer> q = new LinkedList<Integer>();
        	q.add(1);
        	
        	while (q.isEmpty() == false) {
        		int currentRoom = q.poll();
        		ArrayList<Integer> neighborRoom = g.get(currentRoom);
        		
        		for (int i = 0; i < neighborRoom.size(); ++i) {
        			if (nextRoom[neighborRoom.get(i)] == -1) {
        				nextRoom[neighborRoom.get(i)] = currentRoom;
        				q.add(neighborRoom.get(i));
        			}
        		}
        	}
        	
        	System.out.println("Yes");
        	for (int i = 2; i < nextRoom.length; ++i) {
        		System.out.println(nextRoom[i]);
        	}
        }
	}
}