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: Runtime Error)

@file:Suppress("DuplicatedCode")

import java.io.IOException
import java.io.InputStream
import java.io.PrintWriter
import java.util.*

fun main(args: Array<String>) {
    PrintWriter(System.out).use { out ->
        D.solve(D.FastScanner(), out)
        out.flush()
    }
}

private fun D.solve(sc: D.FastScanner, out: PrintWriter) {
    val n = sc.nextInt()
    val m = sc.nextInt()

    val rinsetu = Array(n) { mutableListOf<Short>() }
    val result = ShortArray(n) { -1 }

    repeat(m) {
        val a = sc.nextInt() - 1
        val b = sc.nextInt() - 1
        rinsetu[a].add(b.toShort())
        rinsetu[b].add(a.toShort())
    }

    val queue = ArrayDeque<ShortArray>()
    rinsetu[0].forEach {
        queue.add(shortArrayOf(0, it))
    }
    result[0] = 0

    while (queue.isNotEmpty()) {
        val (from, to) = queue.remove()
        if (result[to.toInt()] >= 0) continue
        result[to.toInt()] = (from + 1).toShort()
        rinsetu[to.toInt()].forEach {
            if (result[it.toInt()] < 0) queue.add(shortArrayOf(to, it))
        }
    }


    out.println("Yes")
    for (i in 1 until n) {
        out.println(result[i])
    }
}

@Suppress("MemberVisibilityCanBePrivate")
private object D {
    private const val zeroCode = '0'.toInt()
    private const val nineCode = '9'.toInt()

    class FastScanner {
        private val `in`: InputStream = System.`in`
        private val buffer = ByteArray(2048)
        private var ptr = 0
        private var buflen = 0

        private fun hasNextByte(): Boolean {
            if (ptr < buflen) {
                return true
            } else {
                ptr = 0
                try {
                    buflen = `in`.read(buffer)
                } catch (e: IOException) {
                    e.printStackTrace()
                }
                if (buflen <= 0) {
                    return false
                }
            }
            return true
        }

        private fun readByte(): Byte = if (hasNextByte()) buffer[ptr++] else -1

        private fun readByteAsInt(): Int = if (hasNextByte()) buffer[ptr++].toInt() else -1

        operator fun hasNext(): Boolean {
            while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++
            return hasNextByte()
        }

        operator fun next(): String {
            if (!hasNext()) throw NoSuchElementException()

            return buildString {
                var b = readByteAsInt()

                while (isPrintableChar(b)) {
                    appendCodePoint(b)
                    b = readByteAsInt()
                }
            }
        }

        fun toCharIterator(): CharIterator = object : CharIterator() {
            private var nextByte: Byte = readByte()

            override fun hasNext(): Boolean = isPrintableChar(nextByte)

            override fun nextChar(): Char {
                val res = nextByte
                nextByte = readByte()
                return res.toChar()
            }

        }

        fun nextLong(): Long {
            if (!hasNext()) throw NoSuchElementException()
            var n: Long = 0
            var minus = false
            var b = readByteAsInt()

            if (b == '-'.toInt()) {
                minus = true
                b = readByteAsInt()
            }

            if (b !in zeroCode..nineCode) {
                throw NumberFormatException()
            }

            while (true) {
                if (b in zeroCode..nineCode) {
                    n *= 10
                    n += b - zeroCode.toLong()
                } else if (b == -1 || !isPrintableChar(b)) {
                    return if (minus) -n else n
                } else {
                    throw NumberFormatException()
                }

                b = readByteAsInt()
            }
        }

        fun nextInt(): Int {
            val nl = nextLong()
            if (nl < Int.MIN_VALUE || nl > Int.MAX_VALUE) throw NumberFormatException()
            return nl.toInt()
        }

        fun nextDouble(): Double {
            return next().toDouble()
        }

        fun readIntArray(n: Int): IntArray {
            val arr = IntArray(n)

            for (i in 0 until n) {
                arr[i] = nextInt()
            }

            return arr
        }

        fun readBigInt(capacity: Int): IntArray {
            if (!hasNext()) throw NoSuchElementException()

            val arr = IntArray(capacity)
            var len = 0
            arr[0] = readByteAsInt() - zeroCode
            while (arr[len] in 0..9) {
                len++
                arr[len] = readByteAsInt() - zeroCode
            }

            return arr.sliceArray(0 until len)
        }

        companion object {
            private inline fun isPrintableChar(c: Int): Boolean {
                return c in 33..126
            }

            private inline fun isPrintableChar(c: Byte): Boolean {
                return c in 33..126
            }
        }
    }

    class BitSet(capacity: Int) {
        val bitset = java.util.BitSet(capacity)

        val cardinality: Int
            get() = bitset.cardinality()

        override fun equals(other: Any?) = (other as? BitSet)?.let { it.bitset == bitset } ?: false

        operator fun set(n: Int, f: Boolean) {
            if (f) {
                bitset.set(n)
            } else {
                bitset.clear(n)
            }
        }

        operator fun get(n: Int) = bitset[n]

        fun trueIterator(startIndex: Int = 0) = object: IntIterator() {
            var nextPos = bitset.nextSetBit(startIndex)

            override fun hasNext() = nextPos in 0 until Int.MAX_VALUE

            override fun nextInt(): Int {
                val value = nextPos
                nextPos = bitset.nextSetBit(nextPos + 1)
                return value
            }
        }

        fun falseIterator(startIndex: Int = 0) = object: IntIterator() {
            var nextPos = bitset.nextClearBit(startIndex)

            override fun hasNext() = nextPos in 0 until Int.MAX_VALUE

            override fun nextInt(): Int {
                val value = nextPos
                nextPos = bitset.nextClearBit(nextPos + 1)
                return value
            }
        }

        fun trueIteratorReversed(startIndex: Int = bitset.length() - 1) = object: IntIterator() {
            var nextPos = bitset.previousSetBit(startIndex)

            override fun hasNext() = nextPos >= 0

            override fun nextInt(): Int {
                val value = nextPos
                nextPos = bitset.previousSetBit(nextPos - 1)
                return value
            }
        }

        fun falseIteratorReversed(startIndex: Int = bitset.length() - 1) = object: IntIterator() {
            var nextPos = bitset.previousClearBit(startIndex)

            override fun hasNext() = nextPos >= 0

            override fun nextInt(): Int {
                val value = nextPos
                nextPos = bitset.previousClearBit(nextPos - 1)
                return value
            }
        }

        fun and(other: BitSet) {
            bitset.and(other.bitset)
        }

        fun or(other: BitSet) {
            bitset.or(other.bitset)
        }

        fun xor(other: BitSet) {
            bitset.xor(other.bitset)
        }

        fun andNot(other: BitSet) {
            bitset.andNot(other.bitset)
        }
    }
}