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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using static Math2;
using static io;
using static Utils;

public class CP {
  List<int>[] edges;
  int[] ans;
  public void Solve() {
    var(N, M) = Cin<int, int>();
    edges = new List<int>[N];
    ans = Enumerable.Repeat(-1, N).ToArray();
    for (int i = 0; i < N; ++i)edges[i] = new List<int>();
    for (int i = 0; i < M; ++i) {
      var(A, B) = Cin<int, int>();
      --A;
      --B;
      edges[A].Add(B);
      edges[B].Add(A);
    }
    var q = new Queue<int>();
    ans[0] = 0;
    q.Enqueue(0);
    while (q.Any()) {
      var v = q.Dequeue();
      foreach (var x in edges[v]) {
        if (ans[x] >= 0)continue;
        ans[x] = v;
        q.Enqueue(x);
      }
    }
    Put("Yes");
    for (int i = 1; i < N; ++i) {
      Put(ans[i] + 1);
    }
  }
}
public static class Math2 {
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const long MOD = 1000000007;
  public const long MOD2 = 998244353;

  public static long Power(long a, long b, long MOD = 1000000007) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0)res = res * a % MOD;
      a = a * a % MOD;
      b >>= 1;
    }
    return res;
  }
  public static long Power2(long a, long b) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0)res = res * a;
      a = a * a;
      b >>= 1;
    }
    return res;
  }
  public static long GCD(long a, long b) {
    while (b > 0) {
      var r = a % b;
      a = b;
      b = r;
    }
    return a;
  }
  public static long LCM(long a, long b) => (b / GCD(a, b)) * a;
  public static long Comb(long n, long r, int MOD = 1000000007) {
    if (r > n - r)r = n - r;
    long Nume = 1;
    long Deno = 1;

    if (r > n - r)r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno = (Deno * i) % MOD;
      Nume = Nume * (n - i + 1) % MOD;
    }
    return (Nume * inv(Deno)) % MOD;
  }
  public static long Comb2(long n, long r) {
    long Nume = 1;
    long Deno = 1;

    if (r > n - r)r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno *= i;
      Nume *= n - i + 1;
    }
    return Nume / Deno;
  }
  public static long inv(long x, int MOD = 1000000007) {
    return Power(x, MOD - 2, MOD);
  }
}
public static class Utils {
  public static void Swap<T>(ref T A, ref T B) {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum(string N) {

    int ret = 0;
    for (int i = 0; i < N.Length; ++i)ret += N[i] - '0';
    return ret;
  }
  public static string ConvertBase(long N, int K) {
    StringBuilder ret = new StringBuilder();
    while (N > 0) {
      var r = N % K;
      N /= K;
      ret.Append(r);
    }
    return new string(ret.ToString().ToCharArray().Reverse().ToArray());
  }
  public static bool NextPermutation<T>(IList<T> lis, Comparison<T> cmp) {
    int n = lis.Count;
    int i = n - 1;
    while (i - 1 >= 0) {
      if (cmp(lis[i - 1], lis[i]) < 0)break;
      --i;
    }
    if (i == 0)return false;
    int j = i;
    while (j + 1 < n) {
      if (cmp(lis[i - 1], lis[j + 1]) > 0)break;
      ++j;
    }
    (lis[i - 1], lis[j]) = (lis[j], lis[i - 1]);
    int k = i;
    int l = n - 1;
    while (k < l) {
      (lis[k], lis[l]) = (lis[l], lis[k]);

      ++k;
      --l;
    }
    return true;
  }
  public static bool NextPermutation<T>(IList<T> lis) => NextPermutation(lis, Comparer<T>.Default.Compare);
}
public class PriorityQueue<T> {
  List<T> _item;
  public int Count { get { return _item.Count; } }
  bool _isascend { get; set; }
  public T Peek { get { return _item[0]; } }
  Comparison<T> Comp;
  public PriorityQueue(bool IsAscend = true, IEnumerable<T> list = null) : this(Comparer<T>.Default.Compare, IsAscend, list) { }
  public PriorityQueue(Comparison<T> cmp, bool IsAscend = true, IEnumerable<T> list = null) {
    _item = new List<T>();
    _isascend = IsAscend;
    this.Comp = cmp;
    if (list != null) {
      _item.AddRange(list);
      Build();
    }
  }

  private int Compare(int i, int j) => (_isascend ? -1 : 1) * Comp(_item[i], _item[j]);
  private void Swap(int i, int j) { var t = _item[i]; _item[i] = _item[j]; _item[j] = t; }
  private int Parent(int i) => (i - 1) >> 1;
  private int Left(int i) => (i << 1) + 1;
  public T Enqueue(T val) {
    int i = _item.Count;
    _item.Add(val);
    while (i > 0) {
      int p = Parent(i);
      if (Compare(i, p) > 0)
        Swap(i, p);
      i = p;
    }
    return val;
  }
  private void Heapify(int index) {
    for (int i = index, j;
      (j = Left(i)) < _item.Count; i = j) {
      if (j != _item.Count - 1 && Compare(j, j + 1) < 0)j++;
      if (Compare(i, j) < 0)
        Swap(i, j);
    }
  }
  public T Dequeue() {
    T val = _item[0];
    _item[0] = _item[_item.Count - 1];
    _item.RemoveAt(_item.Count - 1);
    Heapify(0);
    return val;
  }
  private void Build() {
    for (var i = (_item.Count >> 1) - 1; i >= 0; i--)
      Heapify(i);
  }
  public bool Any() => Count > 0;
}
class Program {
  static void Main(string[] args) {
    var CP = new CP();
    CP.Solve();
  }
}
public static class io {

  public static void Put(string a) => Console.WriteLine(a);
  public static void Put(params object[] i) => Put(string.Join(" ", i));
  public static void Put<T>(IEnumerable<T> a) => Put(string.Join(" ", a));
  public static void PutV<T>(IEnumerable<T> a) { foreach (var z in a)Put(z); }
  public static void YN(bool i) {
    if (i)Put("Yes");
    else Put("No");
  }
  public static string Str => Console.ReadLine();
  public static string[] Strs => Str.Split(" ");
  public static bool IsTypeEqual<T, U>() => typeof(T).Equals(typeof(U));
  public static T ConvertType<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
  public static T Cast<T>(string s) {
    if (IsTypeEqual<T, int>())return ConvertType<T, int>(int.Parse(s));
    else if (IsTypeEqual<T, long>())return ConvertType<T, long>(long.Parse(s));
    else if (IsTypeEqual<T, double>())return ConvertType<T, double>(double.Parse(s));
    else if (IsTypeEqual<T, char>())return ConvertType<T, char>(char.Parse(s));
    else return ConvertType<T, string>(s);
  }
  public static T[] Castarr<T>(string[] s) {

    var ret = new T[s.Length];
    int i = 0;
    if (IsTypeEqual<T, char>()) {
      var list = new List<T>();
      foreach (var t in s) {
        foreach (var u in t) {
          list.Add(ConvertType<T, char>(char.Parse(u.ToString())));
        }
      }
      return list.ToArray();
    }
    foreach (var t in s) {
      if (IsTypeEqual<T, int>())ret[i++] = ConvertType<T, int>(int.Parse(t));
      else if (IsTypeEqual<T, long>())ret[i++] = ConvertType<T, long>(long.Parse(t));
      else if (IsTypeEqual<T, double>())ret[i++] = ConvertType<T, double>(double.Parse(t));
      else ret[i++] = ConvertType<T, string>(t);
    }
    return ret;
  }
  public static T Cin<T>() { var t = Strs; return (Cast<T>(t[0])); }
  public static(T a1, U a2)Cin<T, U>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1])); }
  public static(T a1, U a2, V a3)Cin<T, U, V>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2])); }
  public static(T a1, U a2, V a3, W a4)Cin<T, U, V, W>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3])); }
  public static(T a1, U a2, V a3, W a4, X a5)Cin<T, U, V, W, X>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3]), Cast<X>(t[4])); }
  public static(T a1, U a2, V a3, W a4, X a5, Y a6)Cin<T, U, V, W, X, Y>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3]), Cast<X>(t[4]), Cast<Y>(t[5])); }
  public static(T a1, U a2, V a3, W a4, X a5, Y a6, Z a7)Cin<T, U, V, W, X, Y, Z>() { var t = Strs; return (Cast<T>(t[0]), Cast<U>(t[1]), Cast<V>(t[2]), Cast<W>(t[3]), Cast<X>(t[4]), Cast<Y>(t[5]), Cast<Z>(t[6])); }
  public static T[] Cinarr<T>() { var t = Strs; return Castarr<T>(t); }
  public static T[] CinV<T>(int n) {
    var ret = new T[n];
    for (int i = 0; i < n; ++i) {
      ret[i] = Cin<T>();
    }
    return ret;
  }

  public static T Change<T>(this T x, Func<T, T> f) {
    return f(x);
  }
}