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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;
using static System.Console;
using static System.Math;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            try
            {
                Solve.Answer();
            }
            catch (Exception ex)
            {
                WriteLine(ex.ToString());
            }
        }
    }

    public class Solve
    {
        public static void Answer()
        {
            var nm = IO.ReadSplitInt;
            var nodeList = new List<Node>();
            for (int i = 0; i < nm[0]; i++)
            {
                var node = new Node();
                node.cost = int.MaxValue;
                node.def = false;
                nodeList.Add(node);
            }
            //行先リストを各ノードに格納
            for (int i = 0; i < nm[1]; i++)
            {
                var ab = IO.ReadSplitInt;
                var a = ab[0] - 1;
                var b = ab[1] - 1;
                nodeList[a].AddHash(b);
                nodeList[b].AddHash(a);
            }
            //入口を初期化
            nodeList[0].cost = 0;
            nodeList[0].preNode = -1;

            int cnt = 0;
            bool exist = true;
            while (true)
            {
                int minCost = int.MaxValue;
                int defPoint = 0;
                for (int i = 0; i < nodeList.Count; i++)
                {
                    //確定しているものは除く
                    if (nodeList[i].def) continue;
                    if (minCost > nodeList[i].cost)
                    {
                        minCost = nodeList[i].cost;
                        nodeList[i].def = true;
                        defPoint = i;
                        break;
                    }
                }
                foreach (var anoPoint in nodeList[defPoint].getList())
                {
                    if (nodeList[anoPoint].cost > nodeList[defPoint].cost + 1)
                    {
                        nodeList[anoPoint].cost = nodeList[defPoint].cost + 1;
                        nodeList[anoPoint].preNode = defPoint;
                    }
                }
                bool endFlag = true;
                //foreach (var node in nodeList)
                //{
                //    if (!node.def)
                //    {
                //        endFlag = false;
                //        break;
                //    }
                //}
                if (nodeList.Where(node => node.def == false).Count() > 1) endFlag = false;
                cnt++;
                if (endFlag) break;
                if (endFlag == false && cnt > nm[0] + 10)
                {
                    exist = false;
                    break;
                }
            }
            if (!exist)
            {
                WriteLine("No");
            }
            else
            {
                WriteLine("Yes");
                for (int i = 1; i < nodeList.Count; i++)
                {
                    WriteLine(nodeList[i].preNode + 1);
                }
            }
        }

        public class Node
        {
            // 行先リスト
            HashSet<int> listToAnother = new HashSet<int>();
            // コスト
            public int cost { get; set; }
            // 経路(直前のノード)
            public int preNode { get; set; }
            // 確定したかどうか
            public bool def { get; set; }

            public void AddHash(int x)
            {
                this.listToAnother.Add(x);
            }
            public HashSet<int> getList()
            {
                return this.listToAnother;
            }
        }

        public class IO
        {
            #region Input
            public static string ReadString => ReadLine();
            public static int ReadInt => int.Parse(ReadLine());
            public static long ReadLong => long.Parse(ReadLine());
            public static double ReadDouble => double.Parse(ReadLine());

            public static List<string> ReadSplitString => ReadLine().Split().ToList();
            public static List<int> ReadSplitInt => ReadLine().Split().Select(s => int.Parse(s)).ToList();
            public static List<long> ReadSplitLong => ReadLine().Split().Select(s => long.Parse(s)).ToList();
            public static List<double> ReadSplitdouble => ReadLine().Split().Select(s => double.Parse(s)).ToList();
            #endregion

            #region Output
            public static void OutJoinSpace<T>(IEnumerable<T> list) => WriteLine(string.Join(" ", list));
            public static void WriteLineYes_or_No(bool flag) => WriteLine(flag ? "Yes" : "No");

            #endregion
        }

        public class Mod
        {
            #region
            private readonly static long M = 1000000007;

            public static long Add(long a, long b) => (a * b) % M;
            public static long Sub(long a, long b) => (a - b) % M >= 0 ? (a - b) % M : (a - b) % M + M;
            public static long Multi(long a, long b) => (a * b) % M;
            #endregion
        }

        public static long GCD(long x, long y)
        {
            #region
            if (x < y)
            {
                var tmp = x;
                x = y;
                y = tmp;
            }
            while (true)

            {
                if (x % y == 0)
                {
                    return y;
                }
                else
                {
                    var tmp = x;
                    x = y;
                    y = tmp % y;
                }
            }
            #endregion
        }

        public static long Choice2(long n)
        {
            #region
            if (n <= 1)
                return 0;
            if (n == 2)
                return 1;
            else
                return n * (n - 1) / 2;
            #endregion
        }
    }
}