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 static System.Console;
using static Atcoder_Template_NetCore3.MyUtil;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Numerics;
using System.Threading.Tasks;
using System.IO;

namespace Atcoder_Template_NetCore3
{
    class Program
    {
        static void Main()
        {
            var (roomCount, routeCount) = ReadInt2();
            //便宜上offset1
            var rooms = new Room[roomCount + 1].Select((x, i) => new Room(i)).ToArray();

            for (int i = 0; i < routeCount; i++)
            {
                var (from, to) = ReadInt2();
                rooms[from].CanMoveTo.Add(rooms[to]);
                rooms[to].CanMoveTo.Add(rooms[from]);
            }

            var list = new List<Room>();
            rooms[1].Cost = 0;
            list.Add(rooms[1]);

            for (int currentCost = 1; list.Count > 0; currentCost++)
            {
                var nextList = new List<Room>();
                foreach (var room in list)
                {
                    foreach (var nextRoom in room.CanMoveTo)
                    {
                        if (nextRoom.Cost > currentCost)
                        {
                            nextRoom.Cost = currentCost;
                            nextRoom.MoveTo = room;

                            nextList.Add(nextRoom);
                        }
                    }
                }
                list = nextList;
            }

            WriteLine("Yes");
            var stringBuilder = new StringBuilder();
            for (int i = 2; i < rooms.Length; i++)
            {
                stringBuilder.AppendLine(rooms[i].MoveTo.RoomIndex.ToString());
            }
            Write(stringBuilder.ToString());
        }

        class Room
        {
            public Room(int roomIndex) => RoomIndex = roomIndex;

            public int RoomIndex { get; }

            public List<Room> CanMoveTo { get; } = new List<Room>();

            public Room MoveTo { get; set; }

            public int Cost { get; set; } = int.MaxValue;
        }
    }

    static class MyUtil
    {
        /// <summary>
        /// 指定の桁のビットを取得します。
        /// </summary>
        /// <param name="num"></param>
        /// <param name="count">取得する桁。</param>
        /// <returns></returns>
        public static int GetBit(this int num, int count)
        {
            int mask = (int)Math.Pow(2, count - 1);
            return (num & mask) == 0 ? 0 : 1;
        }

        /// <summary>
        /// <c>int</c>を2進数ビット配列に変換します。
        /// </summary>
        /// <param name="num"></param>
        /// <returns></returns>
        public static int[] ToBitArray(this int num)
        {
            const int size = sizeof(int) * 8;
            var array = new int[size];
            for (int i = 0; i < size; i++)
            {
                array[i] = num.GetBit(size - i);
            }
            return array;
        }

        #region AutoGeneratedCode 整数読み取り系
        public static ValueTuple<int, int> ReadInt2()
        {
            var input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            return (input[0], input[1]);
        }
        public static ValueTuple<long, long> ReadLong2()
        {
            var input = Console.ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
            return (input[0], input[1]);
        }
        public static ValueTuple<int, int, int> ReadInt3()
        {
            var input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            return (input[0], input[1], input[2]);
        }
        public static ValueTuple<long, long, long> ReadLong3()
        {
            var input = Console.ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
            return (input[0], input[1], input[2]);
        }
        public static ValueTuple<int, int, int, int> ReadInt4()
        {
            var input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            return (input[0], input[1], input[2], input[3]);
        }
        public static ValueTuple<long, long, long, long> ReadLong4()
        {
            var input = Console.ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
            return (input[0], input[1], input[2], input[3]);
        }
        public static ValueTuple<int, int, int, int, int> ReadInt5()
        {
            var input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            return (input[0], input[1], input[2], input[3], input[4]);
        }
        public static ValueTuple<long, long, long, long, long> ReadLong5()
        {
            var input = Console.ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
            return (input[0], input[1], input[2], input[3], input[4]);
        }
        public static ValueTuple<int, int, int, int, int, int> ReadInt6()
        {
            var input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            return (input[0], input[1], input[2], input[3], input[4], input[5]);
        }
        public static ValueTuple<long, long, long, long, long, long> ReadLong6()
        {
            var input = Console.ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
            return (input[0], input[1], input[2], input[3], input[4], input[5]);
        }
        public static ValueTuple<int, int, int, int, int, int, int> ReadInt7()
        {
            var input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            return (input[0], input[1], input[2], input[3], input[4], input[5], input[6]);
        }
        public static ValueTuple<long, long, long, long, long, long, long> ReadLong7()
        {
            var input = Console.ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
            return (input[0], input[1], input[2], input[3], input[4], input[5], input[6]);
        }
        #endregion
        /// <summary>
        /// 標準入力からスペース区切りの数値を <see cref="int"/> 配列として読み取ります。
        /// </summary>
        /// <returns></returns>
        public static int[] ReadintArray()
        {
            return ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
        }

        /// <summary>
        /// 標準入力からスペース区切りの数値を <see cref="long"/> 配列として読み取ります。
        /// </summary>
        /// <returns></returns>
        public static long[] ReadlongArray()
        {
            return ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
        }

        /// <summary>
        /// <see cref="IEnumerable{T}"/>の各要素を並べてコンソールに出力します。各要素の間には半角スペースが一つ入ります。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="ts"></param>
        public static void WriteToConsole<T>(this IEnumerable<T> ts)
        {
            StringBuilder stringBuilder = new StringBuilder();
            foreach (T t in ts)
            {
                stringBuilder.Append(t.ToString());
                stringBuilder.Append(" ");
            }
            stringBuilder.Remove(stringBuilder.Length - 1, 1);
            Console.WriteLine(stringBuilder.ToString());
        }
    }
}