Problem:
Score: 400 points

Problem Statement

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.

Sample Input 1

4 4
1 2
2 3
3 4
4 2

Sample Output 1

Yes
1
2
2

If we place the signposts as described in the sample output, the following happens:

Starting in Room 2, you will reach Room 1 after traversing one passage: (2) \to 1. This is the minimum number of passages possible.

Starting in Room 3, you will reach Room 1 after traversing two passages: (3) \to 2 \to 1. This is the minimum number of passages possible.

Starting in Room 4, you will reach Room 1 after traversing two passages: (4) \to 2 \to 1. This is the minimum number of passages possible.

Thus, the objective is satisfied.

Sample Input 2

6 9
3 4
6 1
2 4
5 3
4 6
1 5
6 2
4 5
5 6

Sample Output 2

Yes
6
5
5
1
1

If there are multiple solutions, any of them will be accepted.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Queue;
import java.util.StringTokenizer;

public class Main {

    private static FastScanner scanner = new FastScanner(System.in);

    public static void main(String[] args) {
        int n = scanner.nextInt();
        int m = scanner.nextInt();

        Graph g = new Graph(n);
        for (int i = 0; i < m; i++) {
            int a = scanner.nextInt() - 1;
            int b = scanner.nextInt() - 1;
            g.addEdge(a, b);
            g.addEdge(b, a);
        }
        g.bfs();
    }

    // グラフ
    private static class Graph {
        private Vertex[] vertexes;
        private int size;
        private boolean[] seen;
        private Queue<Vertex> queue = new ArrayDeque<>();

        public Graph(int n) {
            this.size = n;
            this.vertexes = new Vertex[n];
            for (int i = 0; i < n; i++) {
                this.vertexes[i] = new Vertex(i);
            }
            this.seen = new boolean[n];
        }

        public Graph(int[] vertexes) {
            this.size = vertexes.length;
            this. vertexes = new Vertex[vertexes.length];
            for (int i = 0; i < vertexes.length; i++) {
                this.vertexes[i] = new Vertex(vertexes[i]);
            }
            this.seen = new boolean[vertexes.length];
        }

        public void addEdge(int from, int to) {
            this.addEdge(from, to, 0);
        }

        public void addEdge(int from, int to, int weight) {
            this.vertexes[from].addEdge(to, weight);
        }

        public void bfs() {
            Vertex start = vertexes[0];
            seen[0] = true;
            queue.add(start);

            while(!queue.isEmpty()) {
                Vertex v = queue.poll();
                for (Edge e : v.edges) {
                    int next = e.getTo();
                    if (!seen[next]) {
                        seen[next] = true;
                        Vertex nextV = vertexes[next];
                        nextV.value = v.position;
                        queue.add(nextV);
                    }
                }
            }

            boolean isTassei = true;
            for (int i = 1; i < size; i++) {
                if (vertexes[i].value == -1) {
                    isTassei = false;
                }
            }
            if (!isTassei) {
                System.out.println("No");
                return;
            }

            System.out.println("Yes");
            for (int i = 1; i < size; i++) {
                System.out.println(vertexes[i].value + 1);
            }
        }


        // 深さ優先探索を実施し、到達可能な頂点をすべて辿り閉路かどうかをチェックする
        public boolean dfs(int now, int from) {
            this.seen[now] = true;
            boolean isCycle = false;
            for (Edge e : this.vertexes[now].getEdges()) {
                if (e.getTo() == from) {
                    continue;
                }
                if (seen[e.getTo()]) {
                    isCycle = true;
                } else {
                    isCycle = isCycle || dfs(e.getTo(), now);
                }
            }
            return isCycle;
        }

        // 深さ優先探索実施後に到達済みノードかどうかを返す
        public boolean seen(int now) {
            return this.seen[now];
        }

    }

    private static class Vertex {
        public int position;
        public int value;
        public List<Edge> edges = new ArrayList<>();

        public Vertex() {};
        public Vertex(int position) {
            this.position = position;
            this.value = -1;
        }

        public void setValue(int value) {
            this.value = value;
        }

        public void addEdge(int to, int weight) {
            edges.add(new Edge(to, weight));
        }

        public List<Edge> getEdges() {
            return this.edges;
        }
    }

    private static class Edge {
        private int to;
        private int weight;

        public Edge(int to, int weight) {
            this.to = to;
            this.weight = weight;
        }

        public int getTo() {
            return this.to;
        }

        public int getWeight() {
            return this.weight;
        }
    }

    private static class FastScanner {

        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public FastScanner(InputStream in) {
            this.reader = new BufferedReader(new InputStreamReader(in));
        }

        public int[] nextLineToIntArray() {
            String[] stringArray = nextLineToStringArray();
            int[] intArray = new int[stringArray.length];
            for (int i = 0; i < stringArray.length; i++) {
                intArray[i] = Integer.parseInt(stringArray[i]);
            }
            return intArray;
        }

        public String[] nextLineToStringArray() {
            return nextLine().split("");
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
                throw new RuntimeException(e);
            }
        }

        public String next() {
            if (this.tokenizer == null || !this.tokenizer.hasMoreElements()) {
                try {
                    this.tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                    throw new RuntimeException(e);
                }
            }
            return this.tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String[] nextStringArray(int n) {
            String[] stringArray = new String[n];
            for (int i = 0; i < n; i++) {
                stringArray[i] = next();
            }
            return stringArray;
        }

        public int[] nextIntArray(int n) {
            int[] intArray = new int[n];
            for (int i = 0; i < n; i++) {
                intArray[i] = nextInt();
            }
            return intArray;
        }

        public long[] nextLongArray(int n) {
            long[] longArray = new long[n];
            for (int i = 0; i < n; i++) {
                longArray[i] = nextLong();
            }
            return longArray;
        }

        public double[] nextDoubleArray(int n) {
            double[] doubleArray = new double[n];
            for (int i = 0; i < n; i++) {
                doubleArray[i] = nextDouble();
            }
            return doubleArray;
        }
    }
}