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.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt(), m = sc.nextInt();
		Map<Integer, Set<Integer>> map = new HashMap<>();
		for(int i = 1; i <= n; i++){
			map.put(i, new HashSet<Integer>());
		}
		int x, y;
		for(int i = 0; i < m; i++){
			x = sc.nextInt();
			y = sc.nextInt();
			map.get(x).add(y);
			map.get(y).add(x);
		}
		Set<Integer> now = new HashSet<Integer>();
		Set<Integer> tmp = new HashSet<Integer>();
		Set<Integer> zan = new HashSet<Integer>();
		Set<Integer> set = new HashSet<Integer>();
		now.add(1);
		for(int i = 2; i <= n; i++){
			zan.add(i);
		}
		int[] ans = new int[n+1];
		while(zan.size() > 0){
			for(Integer p : now){
				set = map.get(p);
				for(Integer i : set){
					if(ans[i] > 0)continue;
					ans[i] = p;
					zan.remove(i);
					tmp.add(i);
				}
			}
			if(tmp.isEmpty()){
				System.out.println("No");
				return;
			}
			now = tmp;
			tmp = new HashSet<Integer>();
		}
		System.out.println("Yes");
		for(int i = 2; i <= n; i++){
			System.out.println(ans[i]);
		}
	}
}