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++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

/* lib.cpp */

#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <climits>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <stack>
#include <bitset>
#include <queue>
#include <algorithm>
#include <iostream>
#include <iomanip>

#define overload4(_1,_2,_3,_4,name,...) name
#define overload3(_1,_2,_3,name,...) name
#define rep1(n) for(ll i=0;i<n;++i)
#define rep2(i,n) for(ll i=0;i<n;++i)
#define rep3(i,a,b) for(ll i=a;i<b;++i)
#define rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i=(n)-1;i>=0;i--)
#define rrep2(i,n) for(ll i=(n)-1;i>=0;i--)
#define rrep3(i,a,b) for(ll i=(b)-1;i>=(a);i--)
#define rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c)
#define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__)
#define each(i,...) for(auto&& i:__VA_ARGS__)
#define all1(i) begin(i),end(i)
#define all2(i,a) begin(i),begin(i)+a
#define all3(i,a,b) begin(i)+a,begin(i)+b
#define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__)
#define rall1(i) (i).rbegin(),(i).rend()
#define rall2(i,k) (i).rbegin(),(i).rbegin()+k
#define rall3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
#define dsum(...) accumulate(all(__VA_ARGS__),0.0L)
#define elif else if
#define unless(a) if(!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define Sort(a) sort(all(a))
#define Rev(a) reverse(all(a))
#define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a))
#define vec(type,name,...) vector<type> name(__VA_ARGS__)
#define VEC(type,name,size) vector<type> name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,w) vector<vector<type>>name(h,vector<type>(w));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))

using namespace std;
using ll = long long;
using ull = unsigned ll;
using ld = long double;
using pll = pair<ll, ll>;
using graph = vector<vector<int>>;

const ll LINF = 0x1fffffffffffffff;
const ll MINF = 0x1fffffffffff;
const ll INF = 0x3fffffff;
const ll MOD = 1e9 + 7;
const ll MODD = 998244353;
const ld EPS = 1e-9;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
const int edx[8] = {1, 1, 0, -1, -1, -1, 0, 1};
const int edy[8] = {0, 1, 1, 1, 0, -1, -1, -1};

template<class T> inline T min(const vector<T> &v){ return *min_element(all(v)); }
inline char min(const string &v){ return *min_element(all(v)); }
template<class T> inline T max(const vector<T> &v){ return *max_element(all(v)); }
inline char max(const string &v){ return *max_element(all(v)); }
template <class T> inline void chmin(T &a, T b) { a = min(a, b); }
template <class T> inline void chmax(T &a, T b) { a = max(a, b); }

inline int scan(){ return getchar(); }
inline void scan(int &a){ scanf("%d", &a); }
inline void scan(unsigned &a){ scanf("%u", &a); }
inline void scan(long &a){ scanf("%ld", &a); }
inline void scan(long long &a){ scanf("%lld", &a); }
inline void scan(unsigned long long &a){ scanf("%llu", &a); }
inline void scan(char &a){ cin >> a; }
inline void scan(float &a){ scanf("%f", &a); }
inline void scan(double &a){ scanf("%lf", &a); }
inline void scan(long double &a){ scanf("%Lf", &a); }
inline void scan(vector<bool> &vec){ for(unsigned i = 0; i < vec.size(); i++) { int a; scan(a); vec[i] = a; } }
inline void scan(char a[]){ scanf("%s", a); }
inline void scan(string &a){ cin >> a; }
template<class T> inline void scan(vector<T> &vec);
template<class T, size_t size> inline void scan(array<T, size> &vec);
template<class T, class L> inline void scan(pair<T, L> &p);
template<class T, size_t size> inline void scan(T (&vec)[size]);
template<class T> inline void scan(vector<T> &vec){ for(auto &i : vec) scan(i); }
template<class T> inline void scan(deque<T> &vec){ for(auto &i : vec) scan(i); }
template<class T, size_t size> inline void scan(array<T, size> &vec){ for(auto &i : vec) scan(i); }
template<class T, class L> inline void scan(pair<T, L> &p){ scan(p.first); scan(p.second); }
template<class T, size_t size> inline void scan(T (&vec)[size]){ for(auto &i : vec) scan(i); }
template<class T> inline void scan(T &a){ cin >> a; }
inline void in(){}
template <class Head, class... Tail> inline void in(Head &head, Tail&... tail){ scan(head); in(tail...); }
inline void print(){ putchar(' '); }
inline void print(const bool &a){ printf("%d", a); }
inline void print(const int &a){ printf("%d", a); }
inline void print(const unsigned &a){ printf("%u", a); }
inline void print(const long &a){ printf("%ld", a); }
inline void print(const long long &a){ printf("%lld", a); }
inline void print(const unsigned long long &a){ printf("%llu", a); }
inline void print(const char &a){ printf("%c", a); }
inline void print(const char a[]){ printf("%s", a); }
inline void print(const float &a){ printf("%.15f", a); }
inline void print(const double &a){ printf("%.15f", a); }
inline void print(const long double &a){ printf("%.15Lf", a); }
inline void print(const string &a){ for(auto&& i : a) print(i); }
template<class T> inline void print(const vector<T> &vec);
template<class T, size_t size> inline void print(const array<T, size> &vec);
template<class T, class L> inline void print(const pair<T, L> &p);
template<class T, size_t size> inline void print(const T (&vec)[size]);
template<class T> inline void print(const vector<T> &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T> inline void print(const deque<T> &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T, size_t size> inline void print(const array<T, size> &vec){ print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T, class L> inline void print(const pair<T, L> &p){ print(p.first); putchar(' '); print(p.second); }
template<class T, size_t size> inline void print(const T (&vec)[size]){ print(vec[0]); for(auto i = vec; ++i != end(vec); ){ putchar(' '); print(*i); } }
template<class T> inline void print(const T &a){ cout << a; }
inline int out(){ putchar('\n'); return 0; }
template<class T> inline int out(const T &t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> inline int out(const Head &head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }

inline int first(bool i = true){ return out(i?"first":"second"); }
inline int yes(bool i = true){ return out(i?"yes":"no"); }
inline int Yes(bool i = true){ return out(i?"Yes":"No"); }
inline int No(){ return out("No"); }
inline int YES(bool i = true){ return out(i?"YES":"NO"); }
inline int NO(){ return out("NO"); }
inline int Yay(bool i = true){ return out(i?"Yay!":":("); }
inline int possible(bool i = true){ return out(i?"possible":"impossible"); }
inline int Possible(bool i = true){ return out(i?"Possible":"Impossible"); }
inline int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); }
inline void Case(ll i){ printf("Case #%lld: ", i); }

ll modpow(ll a, ll b, ll p = MOD) { ll ret = 1; while (b != 0) { if ((b & 1) == 1) ret *= a; a *= a; if (a >= p) a %= p; if (ret >= p) ret %= p; b >>= 1; } return ret; }
int digit(ll x, ll base = 10) { int ret = 0; while (x) { x /= base; ret++; } return ret; }
int sumOfDigit(ll x, ll base = 10) { int ret = 0; while(x) { ret += x % base; x /= base; } return ret; }
ll factrial(int n) { ll ret = 1; for(int i = 1;i <= n;i++) { ret *= i; } return ret; }
ll gcd(ll a, ll b) { while(b != 0) { a %= b; swap(a, b); } return abs(a); }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
ll modinv(ll a, ll p = MOD) { ll b = p, u = 1, v = 0; while(b) { ll tmp = a / b; a -= tmp * b; u -= tmp * v; swap(a, b); swap(u, v); } u %= p; if (u < 0) u += p; return u; }
bool isprime(ull x) { if(x <= 1) return false; for(int i = 2;i * i <= x;i++) if(x % i == 0) return false; return true; }
map<ll, ll> factor(ull x){ map<ll, ll> ret; for(ll i = 2; i * i <= x; i++) while(x % i == 0){ ret[i]++; x /= i; } if(x != 1) ret[x]++; return ret; }
set<ll> divisor(ull x){ set<ll> ret; for(ll i = 1; i * i <= x; i++) if(x % i == 0){ ret.insert(i); ret.insert(x / i); } return ret; }
ll minDivisor(ull x, ll n = 2) { if(x <= 1) return 1; for(int i = n;i * i <= x;i++) if(x % i == 0) return i; return x; }
ll countDivisor(ull x) { map<ll, ll> m = factor(x); ll ret = 1; for(auto i : m) { ret *= i.second + 1; } return ret; }

class disjoint_set
{
    vector<int> _parent, _size;

public:
    disjoint_set(int n) : _parent(n), _size(n) {
        for (int i = 0; i < n; i++) {
            _parent[i] = i;
            _size[i] = 1;
        }
    }
    int root(int x) {
        if (_parent[x] == x) return x;
        return _parent[x] = root(_parent[x]);
    }
    void unite(int x, int y) {
        int rx = root(x);
        int ry = root(y);
        if (rx == ry) return;
        _parent[rx] = ry;
        _size[ry] += _size[rx];
    }
    bool same(int x, int y) { return root(x) == root(y); }
    int size(int x) { return _size[root(x)]; }
};

void init() { cin.tie(nullptr); cout << fixed << setprecision(15); }

vector<ll> dijkstra(const graph& g, ll n, ll v) {
    priority_queue<pll> q;
    vector<bool> seen(n);
    vector<ll> d(n);
    vector<ll> prev(n);

    rep(i, n) {
        d[i] = INF;
        prev[i] = -1;
    }
    d[v] = 0;
    q.push(mp(0, 0));
    
    while(!q.empty()) {
        ll v = q.top().second;
        q.pop();
        for(auto i : g[v]) {
            if(d[i] > d[v] + 1) {
                d[i] = d[v] + 1;
                prev[i] = v;
                q.push(mp(d[i], i));
            }
        }
    }
    return prev;
}

int solve() {
    LL(n, m);
    graph g(n);
    rep(i, m) {
        INT(a, b);
        a--;b--;
        g[a].push_back(b);g[b].push_back(a);
    }
    vector<ll> p = dijkstra(g, n, 0);
    Yes();
    rep(i, 1, n) {
        out(p[i] + 1);
    }
    
    return 0;
}

int main() { init(); solve(); return 0; }