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.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;

public class Main {
	static List<Set<Integer>> setList = new ArrayList<>();
	static boolean resBool;
	static Integer[] res;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int M = sc.nextInt();
		for (int i = 0; i <= N; i++) {
			Set<Integer> set = new HashSet<>();
			setList.add(set);
		}
		for (int i = 0; i < M; i++) {
			int tmp1 = sc.nextInt();
			int tmp2 = sc.nextInt();
			setList.get(tmp1).add(tmp2);
			setList.get(tmp2).add(tmp1);
		}
		resBool = true;
		res = new Integer[N + 1];
		res[0] = 99;
		res[1] = 99;
		getRes(new ArrayList<>(Arrays.asList(1)));

		if (resBool) {
			System.out.println("Yes");
			for (int i = 2; i <= N; i++) {
				System.out.println(res[i]);
			}
		} else {
			System.out.println("No");
		}
	}

	private static void getRes(List<Integer> array) {
		List<Integer> dist = new ArrayList<>();
		for (int i : array) {
			for (int j : setList.get(i)) {
				if (res[j] == null) {
					dist.add(j);
					res[j] = i;
				}
			}
		}
		if (!Arrays.asList(res).contains(null)) {
			return;
		}
		if (dist.isEmpty()) {
			resBool = false;
			return;
		}
		getRes(dist);
	}
}