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 C# (.NET Core 3.1.201) (judge verdict: Accepted)


using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Diagnostics.Contracts;
using System.Linq;
using System.Text;

namespace at_coder
{
#if TEST
    [TestClass]
#endif
    public class Test_168_d
    {

#if TEST
        public static void Test_Main()
#else
        public static void Main()
#endif
        {
            int N, M;
            ReadInt(out N, out M);
            int[] A = new int[M + 2];
            int[] B = new int[M + 2];

            Dictionary<int, APoint> points = new Dictionary<int, APoint>();
            for(int i=1;i<=N;i++)
            {
                points[i] = new APoint() { No = i };
            }

            for (int i=0;i<M;i++)
            {
                int a, b;
                ReadInt(out a, out b);
                var point_a = points[a];
                var point_b = points[b];
                point_a.Link.Add(b);
                point_b.Link.Add(a);
            }

            var solve = new Solve1();

            solve.Calc(points);

            // すべての点で 到達できているか
            if (points.Values.Max(r => r.Score) < int.MaxValue)
            {
                // 存在するならばそのような配置を  1 つ出力してください。
                Write("Yes");
                foreach(var p in points.Values.OrderBy(r => r.No).Skip(1))
                {
                    Write(p.PrevToTop.ToString());
                }
            }
            else
            {
                Write("No");
            }
        }

        class Solve1
        {
            public void Calc(Dictionary<int,APoint> points)
            {
                // ダイクストラ法で 順番に調査する
                List<int> edgeList = new List<int>();

                edgeList.Add(1);
                points[1].Score = 0;// 到達予定

                while (edgeList.Any())
                {
                    int p = edgeList[0];
                    edgeList.RemoveAt(0);
                    var point = points[p];

                    foreach (int next_p in point.Link)
                    {
                        var point_p = points[next_p];
                        int next_score = point.Score + 1;
                        if (next_score < point_p.Score)
                        {
                            // 経路書き換え
                            point_p.PrevToTop = point.No;
                            point_p.Score = next_score;
                            // 末端追加
                            edgeList.Add(point_p.No);
                        }
                    }
                }
            }
        }
        class APoint
        {
            /// <summary>
            /// １ 番目 ＝ １ 
            /// </summary>
            public int No;

            /// <summary>
            /// その場所に到達するまでのスコア
            /// </summary>
            public int Score = int.MaxValue;
            /// <summary>
            /// リンク
            /// </summary>
            public List<int> Link = new List<int>();
            /// <summary>
            /// １ 番に行くための 最適解
            /// </summary>
            public int PrevToTop;
        }

        private static void Write(string s)
        {
            Console.WriteLine(s);
        }

        private static int[] ReadIntArray()
        {
            string[] ss = Console.ReadLine().Split(new char[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
            int[] ar = new int[ss.Length];
            for (int i = 0; i < ss.Length; i++)
            {
                ar[i] = int.Parse(ss[i]);
            }
            return ar;
        }
        private static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }
        private static void ReadInt(out int a, out int b)
        {
            var ar = ReadIntArray();
            a = ar[0];
            b = ar[1];
        }
        private static void ReadInt(out int a, out int b, out int c)
        {
            var ar = ReadIntArray();
            a = ar[0];
            b = ar[1];
            c = ar[2];
        }
        private static string ReadString()
        {
            return Console.ReadLine();
        }
        private static string[] ReadStringArray()
        {
            string[] ss = Console.ReadLine().Split(new char[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
            return ss;
        }
#if !TEST
    }
}
#endif