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: Accepted)

#ifdef mmlang_source_19_lines

N, M = inputInt(), inputInt()
AB[:M] = inputInt() - 1, inputInt() - 1
AB[M:M * 2] = AB[$1 - M][1], AB[$1 - M][0]
AB.sort()
C[:N] = -1
C[0] = 0
F = queue!(int)()
F.push(0)
for f in F:
    if C[t@AB[:AB.bound(f)][1]] == -1:
        C[t] = C[f] + 1
        F.push(t)
print("Yes")
for f in range(1, N):
    V[:0] = 0, 0
    V.clear()
    V.emplace_back(C[t@AB[:AB.bound(f)][1]], t)
    V.sort()
    print(V[0][1] + 1)

#endif

//#define NDEBUG

#include <cassert>
#include <vector>
#include <deque>
#include <string>
#include <map>
#include <queue>
#include <stack>
#include <algorithm>
#include <cstdlib>
#include <cstdio>
#include <cstring>

using namespace std;

const char*inputCLineOrWord(int mode){static char buf[2097152];static int bufLen=sizeof(buf);static int bufPos=sizeof(buf);static bool canReadFlag=true;static bool crFlag=false;static bool enterFlag=false;if(canReadFlag&&(enterFlag?bufLen<=bufPos:(int)sizeof(buf)<=bufPos+bufPos)){if(0<bufLen-bufPos){memmove(buf,buf+bufPos,bufLen-bufPos);bufLen-=bufPos;}else{bufLen=0;}char*result=fgets(buf+bufLen,sizeof(buf)-bufLen,stdin);canReadFlag=(result!=NULL);if(result!=NULL){int n=strlen(result);enterFlag=(n!=(int)sizeof(buf)-1-bufLen||(1<=bufLen+n&&buf[bufLen+n-1]=='\n'));bufLen+=n;}bufPos=0;}if(mode==0){int pos=bufPos;while(true){char c=buf[pos];if(c==32){buf[pos++]='\0';break;}else if(c==10){if(crFlag){crFlag=false;if(bufPos==pos){pos=++bufPos;continue;}}buf[pos++]='\0';break;}else if(c==13){crFlag=true;buf[pos++]='\0';break;}else if(c==0){break;}++pos;}const char*ret=buf+bufPos;bufPos=pos;while(true){char c=buf[bufPos];if(c==32||c==10||c==13){++bufPos;}else{break;}}return ret;}else if(mode==1){int pos=bufPos;while(true){char c=buf[pos];if(c==10){if(crFlag){crFlag=false;if(bufPos==pos){pos=++bufPos;continue;}}buf[pos++]='\0';break;}else if(c==13){crFlag=true;buf[pos++]='\0';break;}else if(c==0){break;}++pos;}const char*ret=buf+bufPos;bufPos=pos;if(crFlag){while(true){char c=buf[bufPos];if(c==13){++bufPos;crFlag=false;break;}else{break;}}}return ret;}else if(mode==2){return bufLen<=bufPos?NULL:buf+bufPos;}assert(false);return NULL;}const char*inputCWord(){return inputCLineOrWord(0);}int inputInt(){return atoi(inputCWord());}void print_unit(bool val){printf("%s",val?"true":"false");}void print_unit(char val){printf("%c",val);}void print_unit(int val){printf("%d",val);}void print_unit(unsigned int val){printf("%u",val);}void print_unit(size_t val){printf("%zd",val);}void print_unit(const void*val){printf("%p",val);}void print_unit(long long val){printf("%lld",val);}void print_unit(__int128 val){char buf[128];int idx=128;buf[--idx]='\0';bool sign=false;if(val<0){sign=true;val=-val;}while(val){buf[--idx]='0'+(val % 10);val /=10;}if(sign){buf[--idx]='-';}printf("%s",buf+idx);}void print_unit(double val){printf("%g",val);}void print_unit(const char*val){printf("%s",val);}void print_unit(const std::string&val){printf("%s",val.c_str());}template<class T>void print_unit(const std::vector<T>&val){printf("vec(%d) {",(int)val.size());for(int i=0;i<(int)val.size();++i){fputc(' ',stdout);print_unit(val[i]);}printf(" }");}
#define _print0()
#define _print1(e)print_unit(e)
#define _print2(e1,e2)_print1(e1),fputc(' ',stdout),_print1(e2)
#define _print3(e1,e2,e3)_print2(e1,e2),fputc(' ',stdout),_print1(e3)
#define _print4(e1,e2,e3,e4)_print2(e1,e2),fputc(' ',stdout),_print2(e3,e4)
#define _print5(e1,e2,e3,e4,e5)_print3(e1,e2,e3),fputc(' ',stdout),_print2(e4,e5)
#define _print6(e1,e2,e3,e4,e5,e6)_print3(e1,e2,e3),fputc(' ',stdout),_print3(e4,e5,e6)
#define _print7(e1,e2,e3,e4,e5,e6,e7)_print4(e1,e2,e3,e4),fputc(' ',stdout),_print3(e5,e6,e7)
#define _print8(e1,e2,e3,e4,e5,e6,e7,e8)_print4(e1,e2,e3,e4),fputc(' ',stdout),_print4(e5,e6,e7,e8)
#define _print9(e1,e2,e3,e4,e5,e6,e7,e8,e9)_print5(e1,e2,e3,e4,e5),fputc(' ',stdout),_print4(e6,e7,e8,e9)
#define _print10(e1,e2,e3,e4,e5,e6,e7,e8,e9,e10)_print5(e1,e2,e3,e4,e5),fputc(' ',stdout),_print5(e6,e7,e8,e9,e10)
#define _GET_PRINT_MACRO_NAME(_1,_2,_3,_4,_5,_6,_7,_8,_9,_10,NAME,...)NAME
#define print(...)_GET_PRINT_MACRO_NAME(__VA_ARGS__,_print10,_print9,_print8,_print7,_print6,_print5,_print4,_print3,_print2,_print1,_print0)(__VA_ARGS__),fputc('\n',stdout)
#define print0(...)_GET_PRINT_MACRO_NAME(__VA_ARGS__,_print10,_print9,_print8,_print7,_print6,_print5,_print4,_print3,_print2,_print1,_print0)(__VA_ARGS__)
struct _range_ite{int i;int s;_range_ite(int i,int s):i(i),s(s){}bool operator !=(const _range_ite&o)const{return i!=o.i;}void operator++(){i+=s;}const int&operator*()const{return i;}};struct _range_t{int b;int e;int s;_range_t(int b,int e,int s):b(b),e(e),s(s){}_range_ite begin(){return _range_ite(b,s);}_range_ite end(){return _range_ite(e,s);}};_range_t range(int i){return _range_t(0,std::max(0,i),1);}_range_t range(int b,int e){return _range_t(b,std::max(b,e),1);}_range_t range(int b,int e,int s){assert(s!=0);if(0<s){e=b+(std::max(0,e-b-1)/ s+1)*s;}else{e=b+(std::max(0,b-e-1)/-s+1)*s;}return _range_t(b,e,s);}_range_t rrange(int i){return _range_t(std::max(0,i)-1,-1,-1);}_range_t rrange(int b,int e){return _range_t(std::max(b,e)-1,b-1,-1);}_range_t rrange(int b,int e,int s){assert(s!=0);if(0<s){e=b+(std::max(0,e-b-1)/ s+1)*s;}else{e=b+(std::max(0,b-e-1)/-s+1)*s;}return _range_t(e-s,b-s,-s);}
// generated code (by mmlang) :

int N;
int M;
vector<tuple<int, int> > AB;
vector<int> C;
queue<int> F;
vector<tuple<int, int> > V;

int main() {
    {
        const auto & $c1 = inputInt();
        const auto & $c2 = inputInt();
        tie(N, M) = tuple<int, int>($c1, $c2);
    }
    AB.resize(max((int)AB.size(), (int)M)); for(int $1=0, $e=(0<=M ? M : (int)AB.size()+M); $1<$e; ++$1) {
        const auto & $c1 = inputInt() - 1;
        const auto & $c2 = inputInt() - 1;
        AB[$1] = tuple<int, int>($c1, $c2);
    }
    AB.resize(max((int)AB.size(), (int)M * 2)); for(int $e0=M * 2, $1=(0<=M ? M : (int)AB.size()+M), $e=(0<=$e0 ? $e0 : (int)AB.size()+$e0); $1<$e; ++$1) {
        const auto & $c1 = get<1>(AB[$1 - M]);
        const auto & $c2 = get<0>(AB[$1 - M]);
        AB[$1] = tuple<int, int>($c1, $c2);
    }
    sort(AB.begin(), AB.end());
    C.resize(max((int)C.size(), (int)N)); for(int $1=0, $e=(0<=N ? N : (int)C.size()+N); $1<$e; ++$1) C[$1] = -1;
    C[0] = 0;
    F = queue<int>();
    F.push(0);
    while(!(F).empty()) { int f = (F).front(); (F).pop();
        for(auto & $1 : range(lower_bound(AB.begin(), AB.end(), tuple<int, int>(f, -2147483648))-AB.begin(), upper_bound(AB.begin(), AB.end(), tuple<int, int>(f, 2147483647))-AB.begin())) {
            const auto & t = get<1>(AB[$1]);
            if(C[t] == -1) {
                C[t] = C[f] + 1;
                F.push(t);
            }
        }
    }
    print("Yes");
    for(const int & f : range(1, N)) {
        V.resize(max((int)V.size(), (int)0)); for(int $1=0, $e=(0<=0 ? 0 : (int)V.size()+0); $1<$e; ++$1) V[$1] = tuple<int, int>(0, 0);
        V.clear();
        for(auto & $1 : range(lower_bound(AB.begin(), AB.end(), tuple<int, int>(f, -2147483648))-AB.begin(), upper_bound(AB.begin(), AB.end(), tuple<int, int>(f, 2147483647))-AB.begin())) {
            const auto & t = get<1>(AB[$1]);
            V.emplace_back(C[t], t);
        }
        sort(V.begin(), V.end());
        print(get<1>(V[0]) + 1);
    }
    return 0;
}