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.io.*;
import java.nio.charset.StandardCharsets;

public class Main {
	int N, M;
	Node[] nodes;

	static class Node {
		int id;
		int parent = -2;
		Set<Integer> conns;

		Node(int id) {
			this.id = id;
			this.conns = new HashSet<>();
		}
	}

	static class Edge {
		int src, dst;

		Edge(int src, int dst) {
			this.src = src;
			this.dst = dst;
		}
	}

	public static void main(String[] args) throws IOException {
		InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
		BufferedReader in = new BufferedReader(reader);
		Main ins = new Main(in);
		ins.calc();
		ins.showResult();
	}

	Main(BufferedReader in) throws IOException {
		String[] tokens = in.readLine().split(" ");
		N = Integer.parseInt(tokens[0]);
		M = Integer.parseInt(tokens[1]);
		this.nodes = new Node[N];
		for (int i = 0; i < N; ++i) {
			this.nodes[i] = new Node(i);
		}
		for (int i = 0; i < M; ++i) {
			tokens = in.readLine().split(" ");
			int a = Integer.parseInt(tokens[0]) - 1;
			int b = Integer.parseInt(tokens[1]) - 1;
			nodes[a].conns.add(b);
			nodes[b].conns.add(a);
		}
	}

	void mark(int current, int parent) {
		if (nodes[current].parent != -2) {
			return;
		}
		nodes[current].parent = parent;
		for (Integer i : nodes[current].conns) {
			if (i.equals(parent)) {
				continue;
			}
			mark(i, current);
		}
	}

	void calc() {
		Deque<Edge> que = new ArrayDeque<>();
		for (Integer dst : nodes[0].conns) {
			que.add(new Edge(0, dst));
		}
		Set<Integer> markedNodes = new HashSet<>();
		markedNodes.add(0);
		nodes[0].parent = -1;
		while (!que.isEmpty()) {
			Edge edge = que.poll();
			if (!markedNodes.contains(edge.dst)) {
				nodes[edge.dst].parent = edge.src;
				markedNodes.add(edge.dst);
				for (Integer dst : nodes[edge.dst].conns) {
					if (markedNodes.contains(dst)) {
						continue;
					}
					que.add(new Edge(edge.dst, dst));
				}
			}
		}
		System.out.println("Yes");
		for (int i = 1; i < N; ++i) {
			System.out.println((nodes[i].parent + 1));
		}
	}

	void showResult() {
	}

}