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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.PrintWriter
import java.util.*
import java.math.*
import java.lang.*
import kotlin.comparisons.*

val pw = PrintWriter(System.out)
val MOD: Long = (1e+9 + 7).toLong()

data class State(var cur: Int, var num: Int)
fun main(args: Array<String>) {
    val (n, m) = readListOfInt()
    val edges = Array(n) { mutableListOf<Int>() } 
    for(i in 0 until m) {
        val (a, b) = readListOfInt().map { it-1 }
        edges[a].add(b)
        edges[b].add(a)
    }

    val st = ArrayDeque<State>()
    val dirs = Array(n) { State(-1, Int.MAX_VALUE) }.apply {
        this[0].cur = 0
        this[0].num = 0
    }
    st.add(State(0, 0))
    var cnt = 0
    while(!st.isEmpty()) {
        val cur = st.poll()
        val nexts = edges[cur.cur]
        for(next in nexts) {
            cnt++
            if(dirs[next].num >= cur.num + 1) {
                val nState = State(next, cur.num+1)
                dirs[next] = State(cur.cur, cur.num) 
                st.add(nState)
            }
        }
    }
    if(dirs.all { it.cur != -1 }) {
        println("Yes")
        for(i in 1 until dirs.size) {
            val dir = dirs[i]
            println(dir.cur + 1)
        }
    } else {
        println("No")
    }
	pw.flush()
}

/****** Declared Functions and Data Structures ******/
// IO
fun read() = readLine()!!
fun readInt() = read().toInt()
fun readLong() = read().toLong()
fun readDouble() = read().toDouble()
fun readListOfString() = read().split(" ")
fun readListOfInt() = readListOfString().map { it.toInt() }
fun readListOfLong() = readListOfString().map { it.toLong() }
fun readListOfDouble() = readListOfString().map { it.toDouble() }

fun Double.format(digits: Int) = String.format("%.${digits}f", this)
fun Float.format(digits: Int) = String.format("%.${digits}f", this)

fun print(value: Any) { pw.print(value) }
fun println(value : Any) { pw.println(value) }

// Extensions
fun<T> List<T>.toBuckets(): Map<T, Int>
	= this.groupBy { it }.mapValues { it.value.size }

fun<T: Comparable<T>> List<T>.upperBound(element: T, fromIndex: Int=0, toIndex: Int=this.size): Int {
	var l = fromIndex
	var r = toIndex
	while(l < r) {
		val mid = (l+r) / 2
		if(element >= this[mid]) { 
			l = mid + 1
		} else {
			r = mid
		}
	}
	return l
}

fun<T: Comparable<T>> List<T>.lowerBound(element: T, fromIndex: Int=0, toIndex: Int=this.size): Int {
	var l = fromIndex
	var r = toIndex
	while(l < r) {
		val mid = (l+r) / 2
		if(element <= this[mid]) { 
			r = mid
		} else {
			l = mid + 1
		}
	}
	return r 
}

fun <K, V> Map<K, V>.toMutableMap(): MutableMap<K, V> = HashMap(this)

// Util Functions
fun Long.makeDivisors(): List<Long> {
	val divisors = mutableListOf<Long>()
	for(i in 1L .. Math.sqrt(this.toDouble()).toLong()+1L) {
		if(this % i == 0L) {
			divisors.add(i)
			if(i != this/i) {
				divisors.add(this/i)
			}
		}
	}
	return divisors.distinct().sorted()
}

fun Long.isPrime(): Boolean {
	if(this==1L) return false
	for(i in 2L .. Math.sqrt(this.toDouble()).toLong() + 1L) {
		if(this % i == 0L && this != i) {
			return false
		}
	}
	return true
}


fun<T> permutations(src: List<T>): List<List<T>> {
	if(src.size == 1) return listOf(src)
	val perms = mutableListOf<List<T>>()
	val insertElement = src[0]
	permutations(src.drop(1)).forEach { perm ->
		for(i in 0..perm.size) {
			val newPerm = perm.toMutableList()
			newPerm.add(i, insertElement)
			perms.add(newPerm.toList())
		}
	}
	return perms
}

// return nCr, if you want nCr, please access v[n][r]
fun combinations(n: Long): List<List<Long>> {
	val v = (0..n).map { (0..n).map{0L}.toMutableList() }.toMutableList()
	for(i in 0 until v.size) {
		v[i][0] = 1L
		v[i][i] = 1L
	}
	for(i in 0 until v.size) {
		for(j in 1 until i) {
			v[i][j] = (v[i-1][j-1] + v[i-1][j]) % MOD
		}
	}
	return v.map { it.toList() }.toList()
}

fun repeatedModPow(a: Long, n: Long, mod: Long): Long = 
	when {
		n == 0L -> 1L
		n == 1L -> a % mod
		n % 2L == 1L -> (a * repeatedModPow(a, n-1L, mod)) % mod
		else -> {
			val tmp = repeatedModPow(a, n / 2L, mod)
			(tmp * tmp) % mod
		}
	}

// return nCr % MOD
fun modnCkWithoutArray(n: Long, k: Long, mod: Long): Long {
	var ret = 1L
	val min = Math.min(k, n-k)
	// まず分母の計算
	for(i in n downTo (n - min + 1)) {
		ret = ret * i % mod
	}
	for(i in min downTo 1) {
		ret = ret * repeatedModPow(i, (mod - 2L), mod) % mod
	}
	return ret
}

// return nCr % MOD
fun modnCk(n: Int, k: Int, mod: Long): Long {
	val factorials = Array(n+1) { 0L }.apply {
		this[0] = 1L
		if(this.size > 1) this[1] = 1L
	}
	val inverses = Array(n+1) { 0L }.apply {
		this[0] = 1L
		if(this.size > 1) this[1] = 1L
	}
	val factorialInverses = Array(n+1) { 0L }.apply {
		this[0] = 1L
		if(this.size > 1) this[1] = 1L
	}
	for(i in 2 .. n) {
		factorials[i] = (factorials[i-1] * i.toLong() % mod)
		inverses[i] = (mod - inverses[mod.toInt() % i] * (mod / i.toLong()) % mod)
		factorialInverses[i] = (factorialInverses[i-1] * inverses[i] % mod)
	}

	return factorials[n] % mod * (factorialInverses[k] * factorialInverses[n-k] % mod) % mod
}

// should be a >= b
fun gcd(a: Long, b: Long): Long = 
	if(b == 0L) a else gcd(b, a % b)

// shoud be a >= b
fun lcm(a: Long, b: Long): Long = 
	a / gcd(a, b) * b

fun sumDigits(num_: Long): Long {
	var num = num_
	var rtn: Long = 0
	while(num != 0.toLong()) {
		val tmp = num % 10
		rtn += tmp
		num /= 10
	}
	return rtn
}

fun Double.isDecimal(): Boolean = ((this - Math.floor(this)) != 0.0)

// Data Structures

class UnionFind(private val n: Int) {
	private val parent: Array<Int> = Array(n) { 0 }
	private val rank: Array<Int> = Array(n) { 0 }
	private val size: Array<Int> = Array(n) { 0 }

	init {
		for(i in 0 until n) {
			parent[i] = i
			rank[i] = 1
			size[i] = 1
		}
	}

	fun union(u: Int, v: Int) {
		var x = root(u)
		var y = root(v)
		if(x != y) {
			if(rank[y] < rank[x]) {
				val tmp = y 
				y = x
				x = tmp 
			}
			parent[x] = y
			rank[y] += rank[x]
			rank[x] = -1
			val totalSize = size[x] + size[y]
			size[x] = totalSize
			size[y] = totalSize
		}
	}

	fun root(u: Int): Int {
		var x = u
		while(parent[x] != x) {
			x = parent[x]
		}
		return x 
	}

	fun size(u: Int): Int = size[root(u)]
}