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# (Mono-csc 3.5.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Console;

namespace AtCoder_1
{
    class Program
    {
        static List<int>[] pa;
        static Pair<int>[] pairs;
        static void Main(string[] args)
        {
            var nm = CinTAr();
            pairs = new Pair<int>[nm[0]];
            pa = new List<int>[nm[0]];
            for(int i = 0;i < nm[1]; i++)
            {
                
                var AB = CinTAr();
                if(pa[AB[0] - 1] == null)
                {
                    pa[AB[0] - 1] = new List<int>();
                }
                pa[AB[0] - 1].Add(AB[1]);
                if (pa[AB[1] - 1] == null)
                {
                    pa[AB[1] - 1] = new List<int>();
                }
                pa[AB[1] - 1].Add(AB[0]);
            }
            Get(1, 1);
            bool no = false;
            for (int i = 1; i < pairs.Length; i++)
            {
                if (pairs[i].a == 0)
                {
                    no = true;
                    break;
                }
            }

            if (no)
            {
                Cout("No");
            }
            else
            {
                Cout("Yes");
                for (int i = 1; i < pairs.Length; i++)
                {
                    Cout(pairs[i].b);
                }
            }
            Cin();
        }
        static void Get(int now, int dep)
        {
            bool used = false;
            foreach (var nf in pa[now - 1])
            {
                if (pairs[nf - 1].a == 0 || pairs[nf - 1].a > dep)
                {
                    pairs[nf - 1].a = dep;
                    pairs[nf - 1].b = now;
                    used = true;
                    Get(nf, dep + 1);
                }
            }
            if (!used)
            {
                return;
            }
        }

        static Random Rand = new Random();
        static string[] AlphabetTable = new string[] { "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z" };
        static int GetDigits(long num)
        {
            return (int)Math.Floor(Math.Log10(num)) + 1;
        }
        static int GetNumByDigit(long num, int digit)
        {
            return (int)((num / ((int)Math.Pow(10, digit - 1))) % 10);
        }
        static int Loop(int num, int max)
        {
            if (num > max)
            {
                return num % max;
            }
            else if (num < 0)
            {
                return max - (-num) % max;
            }
            else
            {
                return num;
            }
        }
        static long GCD(long a, long b)
        {
            if (a < b) { Swap(ref a, ref b); }
            if (a % b == 0) { return b; }
            else { return GCD(b, a % b); }
        }

        static long LCM(long a, long b)
        {
            return a * b / GCD(a, b);
        }

        static void Swap<T>(ref T a, ref T b)
        {
            T t = a;
            a = b;
            b = t;
        }

        static readonly int MOD10_9_7 = (1000000000 + 7);
        static bool IsInt(double d) { return (int)d == d; }
        static string Cin() { return ReadLine(); }
        static string[] CinAr() { return ReadLine().Split(' '); }
        static int CinT() { return S2i(Cin()); }
        static int[] CinTAr() { return CinAr().Select((x, i) => { return S2i(x); }).ToArray(); }
        static long CinL() { return S2L(Cin()); }
        static long[] CinLAr() { return CinAr().Select((x, i) => { return S2L(x); }).ToArray(); }
        static double CinD() { return S2D(Cin()); }
        static double[] CinDAr() { return CinAr().Select((x, i) => { return S2D(x); }).ToArray(); }
        static int S2i(string s) { return int.Parse(s); }
        static long S2L(string s) { return long.Parse(s); }
        static double S2D(string s) { return double.Parse(s); }
        static void Cout(object s) { WriteLine(s); }
        static long[] Divisor(long n)
        {
            if (n == 1) { return new long[] { 1 }; }
            List<long> res = new List<long>();
            res.Add(1);
            for (long i = 2; i <= n / 2 + 1; i++)
            {
                if (n % i == 0)
                {
                    res.Add(i);
                }
            }
            res.Add(n);
            return res.ToArray();
        }
        static bool IsPrime(long num)
        {
            if (num == 1) { return false; }
            for (long i = 2; i <= Math.Sqrt(num) + 1; i++)
            {
                if (num % i == 0) { return false; }
            }
            return true;
        }

        static void CoutAr<Type>(IEnumerable<Type> types)
        {
            WriteLine(string.Join(" ", types));
        }

        public static long nCr(int n, int r)
        {
            // naive: return Factorial(n) / (Factorial(r) * Factorial(n - r));
            return nPr(n, r) / Factorial(r);
        }

        public static long nPr(int n, int r)
        {
            // naive: return Factorial(n) / Factorial(n - r);
            return FactorialDivision(n, n - r);
        }

        private static long FactorialDivision(int topFactorial, int divisorFactorial)
        {
            long result = 1;
            for (int i = topFactorial; i > divisorFactorial; i--)
                result *= i;
            return result;
        }

        private static long Factorial(int i)
        {
            if (i <= 1)
                return 1;
            return i * Factorial(i - 1);
        }


        public static void CoutMemPairAr<Type>(IEnumerable<Pair<Type>> pairs)
        {
            var ar = pairs.ToArray();
            for(int i = 0;i < ar.Length; i++)
            {
                Console.Write($"({ar[i].a}, {ar[i].b}, {ar[i].c})");
            }
            Console.WriteLine();
        }
    }

    public struct Pair<T>
    {
        public T a;
        public T b;
        public T c;
        public Pair(T _a, T _b) { a = _a; b = _b; c = default(T); }
        public Pair(T _a, T _b, T _c) { a = _a; b = _b; c = _c; }
    }
}