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.Linq;
using System.Runtime.CompilerServices;
using System.Text;

namespace AtCoder
{
    static class Program_E
    {
        class Solver
        {

            private List<int>[] _t;
            private int[] _ms;
            private int _n;
            private int _m;

            public void Solve()
            {
                CreateFromInput();
                //CreateDummy();

                _ms = new int[_n + 1]; // MichiShirube
                _ms[1] = 9999; // tekitou
                var q = new Queue<int>();
                int next = 1;
                do
                {
                    foreach (var t in _t[next])
                    {
                        if (_ms[t] != 0) continue;
                        _ms[t] = next;
                        q.Enqueue(t);
                    }
                    if (q.Count == 0) break;
                    next = q.Dequeue();
                } while (true);

                Wl("Yes");
                for (int i = 2; i <= _n; ++i)
                {
                    Wl(_ms[i].ToString());
                }

            }

            private void CreateFromInput()
            {
                var nm = Ints(0);
                _n = nm[0];
                _m = nm[1];
                _t = new List<int>[_n + 1];
                for (int i = 1; i <= _n; ++i)
                {
                    _t[i] = new List<int>();
                }
                for (int i = 0; i < _m; ++i)
                {
                    var tmp = Ints(0);
                    _t[tmp[0]].Add(tmp[1]);
                    _t[tmp[1]].Add(tmp[0]);
                }
            }
            private void CreateDummy()
            {
                _n = 100000;
                _m = 200000;
                _t = new List<int>[_n + 1];
                for (int i = 1; i <= _n; ++i)
                {
                    _t[i] = new List<int>();
                }
                var r = new Random();
                for (int i = 0; i < _m; ++i)
                {
                    var tmp = new int[] { r.Next(1, _n), r.Next(1, _n) };
                    _t[tmp[0]].Add(tmp[1]);
                    _t[tmp[1]].Add(tmp[0]);
                }
            }
            void Search(int room)
            {
                //Wl(string.Format("room[{0}] : {1}", room, string.Join(",", _t[room].Select(a => a.ToString()).ToArray())));
                foreach (var t in _t[room])
                {
                    if (_ms[t] != 0) continue;
                    _ms[t] = room;
                }
                foreach (var t in _t[room])
                {
                    if (_ms[t] == room) Search(t);
                }
            }




            // ----------------------------------------------------------------------------
            void Wl(string mes)
            {
                Console.WriteLine(mes);
            }
            public int Int()
            {
                return int.Parse(Console.ReadLine());
            }
            public int[] Ints(int subtract)
            {
                return Console.ReadLine().Split(' ').Select(s => int.Parse(s) - subtract).ToArray();
            }
            public Int64[] Int64s(Int64 subtract)
            {
                return Console.ReadLine().Split(' ').Select(s => Int64.Parse(s) - subtract).ToArray();
            }
            public UInt64[] UInt64s(UInt64 subtract)
            {
                return Console.ReadLine().Split(' ').Select(s => UInt64.Parse(s) - subtract).ToArray();
            }


        }



        static void Main(string[] args)
        {
            new Solver().Solve();
        }
    }
    struct ModInt
    {
        const int MOD = 1000000007;
        long Data;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public ModInt(long data) { if ((Data = data % MOD) < 0) Data += MOD; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static implicit operator long(ModInt modInt) => modInt.Data;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static implicit operator ModInt(long val) => new ModInt(val);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator +(ModInt a, ModInt b)
        {
            long res = a.Data + b.Data;
            return new ModInt() { Data = res >= MOD ? res - MOD : res };
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator +(ModInt a, long b) => a.Data + b;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator -(ModInt a, ModInt b)
        {
            long res = a.Data - b.Data;
            return new ModInt() { Data = res < 0 ? res + MOD : res };
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator -(ModInt a, long b) => a.Data - b;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator *(ModInt a, ModInt b) => new ModInt() { Data = a.Data * b.Data % MOD };
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator /(ModInt a, ModInt b) => a.Data * GetInverse(b);

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override string ToString() => Data.ToString();

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static long GetInverse(long a)
        {
            long div;
            long p = MOD;
            long x1 = 1, y1 = 0, x2 = 0, y2 = 1;
            while (true)
            {
                if (p == 1) return x2;
                div = a / p;
                x1 -= x2 * div;
                y1 -= y2 * div;
                a %= p;
                if (a == 1) return x1;
                div = p / a;
                x2 -= x1 * div;
                y2 -= y1 * div;
                p %= a;
            }
        }
    }

}