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 Rust (1.42.0) (judge verdict: Accepted)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};
 
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };
 
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
 
    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
 
    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };
 
    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };
 
    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
 
use std::cmp::Ordering;
use std::cmp;
use std::cmp::min;
use std::collections::BTreeMap;
use std::process;
use std::cmp::Ord;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::VecDeque;
use std::collections::BTreeSet;
use std::mem;
use std::collections::BinaryHeap;
use std::hash::{Hash, Hasher};

// ---------- begin ModInt ----------

#[derive(Clone, Copy)]
struct ModInt(usize);
impl std::ops::Add for ModInt {
    type Output = ModInt;
    fn add(self, rhs: ModInt) -> Self::Output {
        let mut d = self.0 + rhs.0;
        if d >= MODu {
            d -= MODu;
        }
        ModInt(d)
    }
}

impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, rhs: ModInt) {
        *self = *self + rhs;
    }
}

impl std::ops::Sub for ModInt {
    type Output = ModInt;
    fn sub(self, rhs: ModInt) -> Self::Output {
        let mut d = self.0 + MODu - rhs.0;
        if d >= MODu {
            d -= MODu;
        }
        ModInt(d)
    }
}

impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: ModInt) {
        *self = *self - rhs;
    }
}

impl std::ops::Mul for ModInt {
    type Output = ModInt;
    fn mul(self, rhs: ModInt) -> Self::Output {
        ModInt((self.0 as u64 * rhs.0 as u64 % MODu as u64) as usize)
    }
}

impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: ModInt) {
        *self = *self * rhs;
    }
}

impl std::ops::Neg for ModInt {
    type Output = ModInt;
    fn neg(self) -> Self::Output {
        ModInt(if self.0 == 0 {0} else {MODu - self.0})
    }
}

impl std::fmt::Display for ModInt {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl std::str::FromStr for ModInt {
    type Err = std::num::ParseIntError;
    fn from_str(s: &str) -> Result<Self, Self::Err> {
        let val = s.parse::<usize>()?;
        Ok(ModInt::new(val))
    }
}
impl PartialEq for ModInt {
    fn eq(&self, other: &Self) -> bool {
        self.0 == other.0
    }
}
impl Hash for ModInt {
    fn hash<H: Hasher>(&self, state: &mut H) {
        self.0.hash(state);
        self.0.hash(state);
    }
}
impl Eq for ModInt {}
#[allow(dead_code)]
impl ModInt {
    pub fn new(n: usize) -> ModInt {
        ModInt(n % MODu)
    }
    pub fn zero() -> ModInt {
        ModInt(0)
    }
    pub fn one() -> ModInt {
        ModInt(1)
    }
    pub fn pow(self, mut n: usize) -> ModInt {
        let mut t = ModInt::one();
        let mut s = self;
        while n > 0 {
            if n & 1 == 1 {
                t *= s;
            }
            s *= s;
            n >>= 1;
        }
        t
    }
    pub fn inv(self) -> ModInt {
        self.pow(MODu - 2)
    }
}
// ---------- end ModInt ----------

/// Equivalent to std::lowerbound and std::upperbound in c++
pub trait BinarySearch<T> {
    fn lower_bound(&self, x:&T) -> usize;
    fn upper_bound(&self, x:&T) -> usize;
}
 
impl<T: Ord> BinarySearch<T> for VecDeque<T>{
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
 
    fn upper_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less | Ordering::Equal => {
                    low = mid + 1;
                }
                Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}
impl<T: Ord> BinarySearch<T> for [T]{
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
 
    fn upper_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less | Ordering::Equal => {
                    low = mid + 1;
                }
                Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}

fn matmul(A:&Vec<Vec<i64>>, B:&Vec<Vec<i64>>) -> Vec<Vec<i64>>{
    let mut C = vec![vec![0;B[0].len()];A.len()];
    for i in 0..A.len(){
        for k in 0..B.len(){
            for j in 0..B[0].len(){
                C[i][j] += A[i][k]*B[k][j];
                C[i][j] %= MOD;
            }
        }
    }
    return C;
}
fn matpow(A:&mut Vec<Vec<i64>>, n:usize) -> Vec<Vec<i64>>{
    let mut B = vec![vec![0;A.len()];A.len()];
    for i in 0..A.len(){
        B[i][i] = 1;
    }
    let mut n = n;
    let mut tmp = A.clone();
    while(n>0){
        if n&1 == 1{B = matmul(&B, &tmp);}
        tmp = matmul(&tmp, &tmp);
        n>>=1;
    }
    return B;
}

 
 
 

fn divisor(n:usize) -> Vec<usize>{
    let mut res:Vec<usize> = Vec::new(); 
    for i in 1..n+1{
        if i*i>n{break;}
        if n%i == 0{
            res.push(i);
            if i != n/i{
                res.push(n/i);    
            }    
        }    
    }
    res
}
struct UnionFind{
    par:Vec<usize>,
    rank:Vec<usize>,
    size:Vec<usize>,
    size_edge:Vec<usize>,
}
impl UnionFind{
    fn init(n:usize) -> UnionFind{
        let mut par = vec![0;n];
        for i in 0..n{
            par[i] = i;
        }
        UnionFind{
            par:par,
            rank:vec![0;n],
            size:vec![1;n],
            size_edge:vec![0;n],
        }
    }
    fn find(&mut self, x:usize) ->usize{
        if(self.par[x] == x){
            x
        }
        else{
            let p = self.par[x];
            let res = self.find(p);
            self.par[x] = res;
            res
        }
    }
    fn same(&mut self, a:usize, b:usize)->bool{
        self.find(a) == self.find(b)
    }
    fn unite(&mut self, a:usize, b:usize){
        let x = self.find(a);
        let y = self.find(b);
        if x != y{
            if (self.rank[x] < self.rank[y]){
                self.par[x] = y;
                self.size[y] += self.size[x];
                self.size_edge[y] += self.size_edge[x];
                self.size_edge[y] += 1;
            }
            else{
                self.par[y] = x;
                self.size[x] += self.size[y];
                self.size_edge[x] += self.size_edge[y];
                self.size_edge[x] += 1;
                if(self.rank[x] == self.rank[y]){ self.rank[x]+=1;}
            }
            
        }
        else{
            self.size_edge[x] += 1;
        }
    }
    fn check_size(&mut self, a:usize) -> usize{
        let x = self.find(a);
        let s = self.size[x];
        s
    }
}
pub struct Scanner<R> {
    stdin: R,
}
 
impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r')
            .collect::<Vec<_>>();
        std::str::from_utf8(&buf).unwrap()
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
struct LazySegTree<BiOp> {
    n: usize,
    val: Vec<i64>,
    ma:Vec<i64>,
    op: BiOp,
    e: i64,
    upe:i64,
    inf:i64,
}

impl<BiOp> LazySegTree<BiOp>
    where BiOp: Fn(i64, i64) -> i64{
    pub fn new(n_: usize, op: BiOp, e: i64, upe:i64, inf:i64) -> Self {
        let mut n = 1;
        while n < n_ { n *= 2; } // n is a power of 2

        LazySegTree {n: n, val: vec![e; 2 * n ], ma:vec![upe;2*n], op: op, e: e, upe:upe, inf:inf}
    }
    pub fn query(&self, x:usize, y:usize, l:usize, r:usize, k:usize) -> i64 {
        if (r<=x || y<=l) {return self.inf;}
        if (x<=l && r<=y) {return self.ma[k];}
        let mut L = self.query(x,y,l,(l+r)/2, k*2);
        let mut R = self.query(x,y,(l+r)/2,r, k*2+1);
        return self.val[k] + (self.op)(L, R);

    }
    
    pub fn update(&mut self, x:usize, y:usize, v:i64, l:usize,r:usize, k:usize) {
        if (l>=r) {return;}
        if (x<=l && r<=y){
            self.val[k]+=v;
            self.ma[k]+=v;
        }
        else if(l<y && x<r){
            self.update(x, y, v, l, (l+r)/2, k*2);
            self.update(x,y,v,(l+r)/2,r, k*2+1);
            self.ma[k] = self.val[k] + (self.op)(self.ma[k*2], self.ma[k*2+1]);
        }
    }
}
fn modinv(a:ModInt)->ModInt{
    let mut a = a.0 as usize;
    let mut b = MODu as i64;
    let mut u = 1 as i64;
    let mut v = 0 as i64;
    let mut a = a as i64;
    let mut m = MODu as i64;
    while(b>0){
        let mut t = a/b;
        a -= t*b;
        mem::swap(&mut a, &mut b);
        u-=t*v;
        mem::swap(&mut u, &mut v);    
    }
    u%=m;
    if u<0{u+=m;}
    return ModInt(u as usize);

}
fn modpow(x:ModInt, n:ModInt) -> ModInt{
        let mut ans = ModInt(1);
        let mut n = n.0 as usize;
        let mut x = x;
        while(n != 0){
            if (n&1 == 1){ans = ans*x;}
            x = x*x;
            n = n>>1;
        }
        ans
}
fn comb(a:usize, b:usize,  fac:&Vec<ModInt>, ifac:&Vec<ModInt>)->ModInt{
        let mut a = a;
        let mut b = b;
        if a == 0 && b == 0{return ModInt(1);}
        if a<b || a<0{return ModInt(0);}
        let mut tmp = ifac[a-b]*ifac[b];
        return tmp * fac[a];
}

fn invs()->(Vec<ModInt>, Vec<ModInt>){
    let mut fac = vec![ModInt(0);300001];
    let mut ifac = vec![ModInt(0);300001];
    fac[0] = ModInt(1);
    ifac[0] = ModInt(1);
    for i in 0..300000{

        fac[i+1] = fac[i] * ModInt(i+1);
        ifac[i+1] = ifac[i] * modpow(ModInt(i+1), ModInt(MODu - 2));
    }
    (fac, ifac)
}

struct ConvexHallTrick {
    Q: Vec<(i64, i64)>,
}

impl ConvexHallTrick{
    pub fn new() -> Self {

        ConvexHallTrick {Q: Vec::new()}
    }
    pub fn calc(&self, p:(i64, i64), x:i64)->i64{
        return p.0 * x + p.1;
    }
    pub fn dodo(& self, A:(i64, i64), B:(i64, i64), C:(i64, i64)) -> bool{
        //max or min
        (A.1 - C.1) * (B.0 - A.0) <= (A.1 - B.1)*(C.0 - A.0)
    }
    pub fn add(&mut self, a:i64, b:i64){
        self.Q.push((a, b));
        let mut v = self.Q.len();
        while(v >=3 && self.dodo(self.Q[v-3], self.Q[v-2], self.Q[v-1])){
            self.Q[v-2] = self.Q[v-1];
            self.Q.pop();
            v = self.Q.len();
        }
    }
    pub fn query(& self, x:i64) -> i64{
        let mut L = -1;
        let mut R = (self.Q.len() - 1) as i64;
        while(R-L>1){
            let mut m = (L+R)/2;
            if self.calc(self.Q[m as usize], x)>=self.calc(self.Q[m as usize+1], x){
                L=m;
            }
            else{
                R=m;
            }

        }
        return self.calc(self.Q[R as usize], x);
    }
}
#[derive(Eq, PartialEq, Clone, Debug)]
pub struct Rev<T>(pub T);
impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}
impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}
fn sieve(n:usize) -> (Vec<bool>, Vec<usize>){
    let mut p:usize = 0;
    let mut is_prime = vec![false; n+1];
    let mut prime = Vec::new();
    for i in 0..n+1{
        is_prime[i] = true;
    }
    is_prime[0] = false;
    is_prime[1] = false;
    for i in 2..n+1{
        if is_prime[i]{
            prime.push(i as usize);
            let mut j = 2*i;
            while(j<=n){
                is_prime[j] = false;
                j+=i;
            }
        }
    }
    (is_prime, prime)
    
}
fn nHr(n:usize, r:usize, fac:&Vec<ModInt>, ifac:&Vec<ModInt>) -> ModInt{
    comb(n + r - 1, r, fac, ifac)
}
fn gcd(a:usize, b:usize)->usize{
    if b==0{return a;}
    return gcd(b, a%b);
}
fn lcm(a:usize, b:usize)->usize{
    return (b/gcd(a, b))*a;
}
struct SegTree_MOD<BiOp> {
    n: usize,
    dat: Vec<i64>,
    op: BiOp,
    e: i64,
    mod_:i64,
}
impl<BiOp> SegTree_MOD<BiOp>
    where BiOp: Fn(i64, i64) -> i64 
          {
    pub fn new(n_: usize, op: BiOp, e: i64, mod_:i64) -> Self {
        let mut n = 1;
        while n < n_ { n *= 2; } // n is a power of 2
        SegTree_MOD {n: n, dat: vec![e; 2 * n - 1], op: op, e: e, mod_:mod_}
    }
    /* ary[k] <- v */
    pub fn update(&mut self, idx: usize, v: i64) {
        let mut k = idx + self.n - 1;
        self.dat[k] = v;
        while k > 0 {
            k = (k - 1) / 2;
            self.dat[k] = (self.op)(self.dat[2 * k + 1], self.dat[2 * k + 2]);
            self.dat[k] %= self.mod_;
        }
    }
    /* [a, b) (note: half-inclusive)
     * http://proc-cpuinfo.fixstars.com/2017/07/optimize-segment-tree/ */
    pub fn query(&self, mut a: usize, mut b: usize) -> i64 {
        let mut left = self.e;
        let mut right = self.e;
        a += self.n - 1;
        b += self.n - 1;
        while a < b {
            if (a & 1) == 0 {
                left = (self.op)(left, self.dat[a]);
                left %= self.mod_;
            }
            if (b & 1) == 0 {
                right = (self.op)(self.dat[b - 1], right);
                right %= self.mod_;
            }
            a = a / 2;
            b = (b - 1) / 2;
        }
        let mut res = (self.op)(left, right);
        res %= self.mod_;
        res
        
    }
}
fn modpow2(x:usize, n:usize) -> usize{
        let mut ans = 1;
        let mut n = n;
        let mut x = x;
        while(n != 0){
            if (n&1 == 1){ans = ans*x%13;}
            x = x*x%13;
            n = n>>1;
        }
        ans
}
#[derive(Clone)]
struct PPUnionFind{
    par:Vec<usize>,
    rank:Vec<usize>,
    time:Vec<usize>,
    now:usize,
    history:Vec<(usize, usize)>,
}
impl PPUnionFind{
    fn init(n:usize) -> PPUnionFind{
        let mut par = vec![0;n];
        for i in 0..n{
            par[i] = i;
        }
        PPUnionFind{
            par:par,
            rank:vec![0;n],
            time:vec![INF as usize;n],
            now:0,
            history:vec![],
        }
    }
    fn find(&mut self, t:usize, x:usize) ->usize{
        if self.time[x] > t{return x;}
        else { let tt = self.par[x]; return self.find(t, tt);}
    }
    fn unite(&mut self, x:usize, y:usize) -> usize{
        self.now+=1;
        let mut x = x;
        let mut y = y;
        let nc = self.now;
        x = self.find(nc, x);
        y = self.find(nc, y);
        if x == y{return self.now;}
        if self.par[x] < self.par[y] {mem::swap(&mut x, &mut y);}
        self.par[x] += self.par[y];
        self.history.push((self.now, self.par[x]));
        self.par[y] = x;
        self.time[y] = self.now;
        return self.now;
    }
}

fn prim(cost:&Vec<Vec<(usize, i64)>>, vs:usize)->i64{
    let mut used = vec![false; vs];
    let mut bh = BinaryHeap::new();
    for j in 0..cost[0].len(){
            bh.push((cost[0][j].1, cost[0][j].0));
    }
    used[0] = true;
    let mut res = 0;
    while(bh.len()!=0){
        let mut m = bh.pop().unwrap();
        if used[m.1]{continue;}
        used[m.1] = true;
        for e in 0..cost[m.1].len(){
            if used[cost[m.1][e].0] == false{
                bh.push((cost[m.1][e].1, cost[m.1][e].0));
            }
        }
        res += m.0;
    }
    return res;
}
fn kruscal(cost:&mut Vec<(i64, usize, usize)>, vs:usize)->i64{
    cost.sort();
    let mut uf = UnionFind::init(vs);
    let mut res = 0;

    for i in 0..cost.len(){
        let e = cost[i].clone();
        if uf.find(e.1) != uf.find(e.2){
            uf.unite(e.1, e.2);
            res += e.0;
        }
    }
    return res;
}
fn kruscal3(cost:&mut Vec<(f64, usize, usize, usize)>, vs:usize)->(UnionFind, Vec<usize>) {
    cost.sort_by(|a, b| (&a.0).partial_cmp(&b.0).unwrap());
    let mut uf = UnionFind::init(vs);
    let mut res = 0.0;
    let mut rv = Vec::new();
    let mut c = 0.0;
    let mut t = 0.0;
    for i in 0..cost.len(){
        let e = cost[i].clone();
        if uf.find(e.1) != uf.find(e.2){
            uf.unite(e.1, e.2);
            rv.push(e.3);
        }
    }
    return (uf,rv);
}
fn kruscal2(cost:&mut Vec<(f64, usize, usize)>, vs:usize)->f64{
    cost.sort_by(|a, b| (&a.0).partial_cmp(&b.0).unwrap());
    let mut uf = UnionFind::init(vs);
    let mut res = 0.0;
    for i in 0..cost.len(){
        let e = cost[i].clone();
        if uf.find(e.1) != uf.find(e.2){
            uf.unite(e.1, e.2);
            res+= e.0;
        }
    }
    return res;
}

struct segtree<I, Op>{
    n: usize,
    dat: Vec<I>,
    op:Op,
    e:I,
}
impl<I, Op> segtree<I, Op>


    where Op: Fn(I, I) -> I, I:Copy{
        
        pub fn new(n_:usize, op: Op, e:I)->Self{
            let mut n = 1;
            while(n<n_){n*=2;}
            segtree{n: n, dat:vec![e; 2*n-1], op:op, e:e}
        }
        pub fn update(&mut self, k:usize, a:I){
            let mut k = k;
            k += self.n-1;
            self.dat[k] = a;
            while(k>0){
                k = (k-1)/2;
                self.dat[k] = (self.op)(self.dat[k*2 + 1], self.dat[k*2+2]);
            }
        }
        pub fn query(&self, a:usize, b:usize, k:usize, l:usize, r:usize) -> I{
            if r<=a || b<=l{return self.e;}
            if a<=l && r<=b{return self.dat[k];}
            else{
                let mut vl = self.query(a, b, k*2+1, l, (l+r)/2);
                let mut vr = self.query(a, b, k*2+2, (l+r)/2, r);
                return (self.op)(vl, vr);
            }
        }
    }
struct BIT<I, Op>{
    n:usize,
    bit:Vec<I>,
    op:Op,
    e:I,
    ini:I,
}
impl <I, Op>  BIT<I, Op>
    /* 1-index*/  
    where Op: Fn(I, I) -> I, I:Copy{
        pub fn new(n_:usize, op:Op, e:I, ini:I)->Self{
            BIT{n:n_, bit:vec![e;n_+1], op:op, e:e, ini:ini}
        }
        pub fn sum(&self, i:usize)->I{
            let mut s = self.ini;
            let mut i = i as i64;
            while(i>0){
                s = (self.op)(s, self.bit[i as usize]);
                i -= i & -i;
            }
            return s;
        }
        pub fn add(&mut self, i:usize, x:I){
            let mut i = i as i64;
            while(i<=self.n as i64){
                self.bit[i as usize] = (self.op)(self.bit[i as usize], x);
                i += i & -i;
            }
        }
    }
struct Dsegtree{
    n: usize,
    datA: Vec<i64>,
    datB:Vec<i64>,
    e:i64,
}
impl Dsegtree{
        pub fn new(n_:usize, e:i64)->Self{

            Dsegtree{n:n_, datA:vec![e; 1<<22 - 1], datB:vec![e;1<<22 - 1], e:e}
        }
        pub fn update(&mut self,a:usize, b:usize, x:i64,  k:usize, l:usize, r:usize){
            //println!("{} {} {} {} {} {}", a, b, x, k , l, r);
            if a<=l && r<=b{
                self.datA[k] += x;
            }
            else if (l<b && a<r){
                self.datB[k] += (cmp::min(b, r) as i64 - cmp::max(a, l) as i64) * x;
                self.update(a, b, x, k*2+1, l, (l+r)/2);
                self.update(a, b, x, k*2+2, (l+r)/2, r);
            }
        }
        pub fn query(&self, a:usize, b:usize, k:usize, l:usize, r:usize) -> i64{
            if (b<=l || r<=a){
                return 0;
            }
            else if (a<=l && r<=b){
                return self.datA[k] * ((r as i64-l as i64)) + self.datB[k];
            }
            else{
                let mut res = (cmp::min(b, r) as i64 - cmp::max(a, l) as i64)* self.datA[k];
                res += self.query(a, b, k*2+1, l, (l+r)/2);
                res += self.query(a, b, k*2+2, (l+r)/2, r);
                return res;
            }
        }
    }
/*
unwrap_or_else
*/
fn prime_factor(n:usize)->HashMap<usize, usize>{
    let mut res = HashMap::new();
    let mut n = n;
    for i in 2..n{
        if i*i>n{break;}
        while(n%i==0){
            *res.entry(i).or_insert(0)+=1;
            n/=i;
        }
    }
    if n != 1{
        res.insert(n, 1);
    }
    res
}
struct rollinghash{
    base:Vec<i64>,
    Mod:Vec<i64>,
    hash:Vec<Vec<i64>>,
    power:Vec<Vec<i64>>,
}
impl rollinghash{
    pub fn new(s:&Vec<usize>)->Self{
        let mut n = s.len();
        let mut base = vec![1007, 2009];
        let mut hash = vec![vec![0;n+1];2];
        let mut power = vec![vec![1;n+1];2];
        let mut Mod = vec![1000000007, 1000000009];
        for iter in 0..2{
            let mut ht = vec![0;n+1];
            let mut pt = vec![1;n+1];
            for i in 0..n{
                hash[iter][i+1] = (hash[iter][i] * base[iter] + s[i] as i64) % Mod[iter];
                power[iter][i+1] = power[iter][i] * base[iter] % Mod[iter];
            }
        }
        return rollinghash{base:base, Mod:Mod, hash:hash, power:power}
   
    }
    pub fn get(&self, l:usize, r:usize)->(i64, i64){
        let mut res = self.hash[0][r] - self.hash[0][l] * self.power[0][r-l] % self.Mod[0];
        if res<0{
            res += self.Mod[0];
        }
        let mut res2 = self.hash[1][r] - self.hash[1][l] * self.power[1][r-l] % self.Mod[1];
        if res2<0{
            res2 += self.Mod[1];
        }
        return (res, res2);
    }

}
struct LCA{
    G:Vec<Vec<i64>>,
    parent:Vec<Vec<i64>>,
    depth:Vec<i64>,
    root:i64,
}
impl LCA{
    pub fn new(G:Vec<Vec<i64>>, N:i64,R:i64)->Self{
        let D = (f64::log2(N as f64)) as i64 + 2;
        LCA{G:G, parent:vec![vec![0;N as usize];1+D as usize], depth:vec![0;N as usize], root:R}
    }
    pub fn getP(&mut self, v:i64, p:i64, d:i64){
        self.parent[0][v as usize] = p;
        self.depth[v as usize] = d;
        for i in 0..self.G[v as usize].len(){
            if self.G[v as usize][i as usize] != p{
                let n = self.G[v as usize][i as usize];
                self.getP(n, v, d+1);
            }
        }
    }
    pub fn init(&mut self){
        let root = self.root;
        self.getP(root, -1, 0);
        let V = self.depth.len();
        let logN = f64::log2(V as f64) as i64 + 2;
        for k in 0..logN{
            for v in 0..V{
                if self.parent[k as usize][v as usize] <0{
                    self.parent[k as usize+1][v as usize] = -1;
                }
                else{
                    self.parent[k as usize+1][v as usize] = self.parent[k as usize][ (self.parent[k as usize][v as usize]) as usize];
                }
            }
        }
    }
    fn ft(&self, f:i64, d:i64)->i64{
        let mut now = f;
        let mut now2 = 0;
        let V = self.depth.len();

        let logN = f64::log2(V as f64) as i64 + 2;
        let mut v = f;
        for k in 0..logN{
            if (d >> k) & 1 == 1{
                v = self.parent[k as usize][v as usize];
            }
        }

        return v;
    }

    fn lca(&mut self,u:i64, v:i64)->i64{
        let mut u = u;
        let mut v = v;
        if self.depth[u as usize] > self.depth[v as usize]{
            mem::swap(&mut u, &mut v);
        }
        let mut V = self.depth.len();
        let logN = f64::log2(V as f64) as i64 + 2;
        for k in 0..logN{
            if ((self.depth[v as usize] - self.depth[u as usize]) >> k)&1 == 1{
                v = self.parent[k as usize][v as usize];
            }
        }
        if u == v{return u;}
        for k in (0..logN).rev(){
            if self.parent[k as usize][u as usize] != self.parent[k as usize][v as usize]{
                u = self.parent[k as usize][u as usize];
                v = self.parent[k as usize][v as usize];
            }
        }
        return self.parent[0][u as usize];
    }

    fn dist(&mut self,u:i64, v:i64)->i64{
        let lc = self.lca(u, v);
        return self.depth[u as usize] + self.depth[v as usize] - 2* self.depth[lc as usize];
    }

}
fn fast_prime_factor_table(ma:usize)->Vec<usize>{
    let mut p = sieve(1001);
    let mut minf = vec![0;ma];
    for j in 0..p.1.len(){
        let P = p.1[j];
        let mut now = P;
        for i in 2..ma{
            if minf[now] ==0{
                minf[now] = P;
            }
            now+=P;
            if now>=ma{
                break;
            }
        }
    }
    return minf;
}
fn area_rectanble(x1:f64, x2:f64, x3:f64, y1:f64, y2:f64, y3:f64)->f64{
    let tmp = x1*y2 + x2*y3 + x3*y1 - y1*x2 - y2*x3 - y3*x1;
    tmp.abs()/2.0
}
#[derive(PartialEq, Clone)]
struct FW(f64);

impl Eq for FW {}

impl PartialOrd for FW {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        self.0.partial_cmp(&other.0)
    }
}

impl Ord for FW {
    fn cmp(&self, other: &FW) -> Ordering {
        other.partial_cmp(self).unwrap()

    }
}
/* parsing
    fn expr(s:&Vec<char>, i:&mut usize) -> Vec<usize>{
        let mut val = term(s, i);
        while(*i<s.len() && (s[*i] == '+' || s[*i] == '-')){
            let mut op = encode(s[*i]);
            *i+=1;
            let mut val2 = term(s, i);
            val = cal(val, val2, op);
        }
        return val;
    }
    fn term(s:&Vec<char>, i:&mut usize) -> Vec<usize>{
        let mut val = factor(s, i);
        while(*i<s.len() && s[*i] == '*'){
            let mut op = encode(s[*i]);
            *i+=1;
            let mut val2 = factor(s, i);
            val = cal(val, val2, op);
        }
        return val;
    }
    fn factor(s:&Vec<char>, i:&mut usize)->Vec<usize>{
        if s[*i] == 'R' || s[*i] == 'S' || s[*i] == 'P' || s[*i] == '?'{
            let mut res = encode(s[*i]);
            *i+=1;
            return res;
        }
        *i+=1;
        let mut ret = expr(s, i);
        *i+=1;
        return ret;
    }
*/
fn matmulf64(A:&Vec<Vec<f64>>, B:&Vec<Vec<f64>>) -> Vec<Vec<f64>>{
    let mut C = vec![vec![0.0;B[0].len()];A.len()];
    for i in 0..A.len(){
        for k in 0..B.len(){
            for j in 0..B[0].len(){
                C[i][j] += A[i][k]*B[k][j];
            }
        }
    }
    return C;
}
//sort_by_key(|a| vec![a[0], -a[1]]);
//sort_by_key(|a| vec![a[0], -a[1]]);
////v.sort_by(|a, b| a.partial_cmp(b).unwrap());
struct UnionFind2 {
    par: Vec<usize>,
    rank: Vec<usize>,
}

impl UnionFind2 {
    fn new(n: usize) -> UnionFind2 {
        let mut vec = vec![0;n];
        for i in 0..n {
            vec[i] = i;
        }
        UnionFind2 {
            par : vec,
            rank : vec![0;n],
        }
    }

    fn find(&mut self, x: usize) -> usize {
        if x == self.par[x] {
            x
        }else{
            let par = self.par[x];
            let res = self.find(par);
            self.par[x] = res;
            res
        }
    }

    fn same(&mut self, a: usize, b: usize) -> bool {
        self.find(a) == self.find(b)
    }

    fn unite(&mut self, a: usize, b: usize){
        let apar = self.find(a);
        let bpar = self.find(b);
        if self.rank[apar] > self.rank[bpar] {
            self.par[bpar] = apar;
        }else{
            self.par[apar] = bpar;
            if self.rank[apar] == self.rank[bpar] {
                self.rank[bpar] += 1;
            }
        }
    }
}





#[macro_use]
fn solve(){
    let sssss = std::io::stdin();
    let mut sc = Scanner { stdin: sssss.lock() };
    /*
    let mut N:usize = sc.read();
    let mut M:usize = sc.read();
    let mut prob = vec![vec![INF as i64;N];M];
    let mut c = vec![];
    for i in 0..M{
        let mut x:usize = sc.read();
        let mut C:usize = sc.read();
        c.push(C);
        for j in 0..x{
            let mut w:usize = sc.read();
            let mut p:i64 = sc.read();
            prob[i][w-1] = p;
        }
    }
    */
    let mut N:usize = sc.read();
    let mut M:usize = sc.read();
    let mut a = vec![];
    let mut b = vec![];
    for i in 0..M{
        let mut A:usize = sc.read();
        let mut B:usize = sc.read();
        a.push(A);
        b.push(B);
    }
    let mut g = vec![vec![];N];
    for i in 0..M{
        g[a[i]-1].push(b[i]-1);
        g[b[i]-1].push(a[i]-1);
    }
    let mut res = vec![N+1;N];
    let mut now = BinaryHeap::new();
    now.push((0i64, 0));
    res[0] = 0;
    while(now.len() != 0){
        let mut t = now.pop().unwrap();
        let mut v = t.1;
        let mut d = t.0*-1;

        for i in 0..g[v].len(){
            if res[g[v][i]] == N+1{
                res[g[v][i]] = v;
                now.push(((d+1)*-1, g[v][i]));
            }
        }
    }
    println!("Yes");
    for i in 1..N{
        println!("{}", res[i]+1);
    }






}






fn main(){
    solve();
}
const PI:f64 = std::f64::consts::PI;
pub static MOD:i64 = 998244353;
pub static MODu:usize = 998244353;
pub static eps:f64 = 1e-6;
const INF: i64 = 1 << 60;