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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

require 'set'
# require 'active_support'
# require 'active_support/core_ext'

def main
    n,m = gets.chomp.split(" ").map(&:to_i)
    abs = m.times.map {gets.split(" ").map(&:to_i)}
    # p n,m
    # p abs
    # n,m = 6,9
    # abs = [[3, 4], [6, 1], [2, 4], [5, 3], [4, 6], [1, 5], [6, 2], [4, 5], [5, 6]]

    ans = Array.new(n+1, 0)
    found = [1]
    found2 = [1]
    found3 = [1]
    while found3.size < n
        found.each do |room|
            delete_list = []
            # puts ""
            # puts 'found'
            # p found
            # puts "room: #{room}"
            (0...abs.size).each do |i|
                if (abs[i].include? room) && found3.index(abs[i][1-abs[i].index(room)]).nil?
                    # puts "abs[i]: #{abs[i]}"
                    found2.push abs[i][1-abs[i].index(room)]
                    found3.push abs[i][1-abs[i].index(room)]
                    ans[abs[i][1-abs[i].index(room)]] = room
                    delete_list.push(i)
                end
            end
            found2.delete(room)
            delete_list.reverse_each do |i|
                abs.delete_at(i)
            end
            # puts "found"
            # p found
        end
        # found = found2.deep_dup
        found = Marshal.load(Marshal.dump(found2))
        # puts 1
        # p found
        # puts 2
        # p found2
        # puts 3
        # p found3
        # puts "ans"
        # p ans
    end
    puts 'Yes'
    puts ans[2..-1]
end

main

## イディオムなど
# until s.empty? do
#
## 配列のインデックス
# s[0,6] # 0番目から6文字
# s[0..6] # 0番目から6番目まで
# s[5..-1] # 5番目から最後まで
#
## 全探索
# [0, 1].repeated_permutation(n) do |combination| # 2^n の全探索
# array.combination(i) do |selected| # array から要素が i 個である部分列を全部抽出