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 (Python):
N,M = map(int,input().split())
adjacent = [[] for i in range(N)]
for i in range(M):
  A,B = map(int,input().split())
  adjacent[A-1].append(B-1)
  adjacent[B-1].append(A-1)
Michi = [0 for i in range(N)]
visited = set()
frontier = set()
visited.add(0)
frontier.add(0)
while len(frontier) > 0:
  newfrontier = set()
  for v in frontier:
    for next in adjacent[v]:
      if next not in visited:
        Michi[next] = v
        visited.add(next)
        newfrontier.add(next)
  frontier = newfrontier
print('Yes')
for i in range(1,N):
  print(Michi[i]+1)

Solution (Python):
from collections import deque
import sys
input = sys.stdin.readline
N,M = map(int,input().split())
ki=[[] for f in range(N)]
for i in range(M):
 A,B= map(int,input().split())
 ki[A-1].append(B-1)
 ki[B-1].append(A-1)
stack = deque([0])
check = [0]*N 
check[0] = 1
ans=[0]*(N-1)
while stack != deque([]) :
 a=stack.popleft()
 for i in range(len(ki[a])):
  if check[ki[a][i]]==0:
   stack.append(ki[a][i])
   check[ki[a][i]]=1
   ans[ki[a][i]-1]=a+1
print("Yes")
for i in range(N-1):
 print(ans[i])

Solution (Python):
n, m = map(int, input().split())

graph = [[] for _ in range(n+1)]

for i in range(m):
    a, b = map(int, input().split())
    graph[a].append(b)
    graph[b].append(a)


milestone = [0] * (n+1)
q = []
q.append(1)
while len(q) != 0:
    for i in graph[q[0]]:
        if milestone[i] == 0:
            milestone[i] = q[0]
            q.append(i)
    q.pop(0)

print("Yes")
for i in range(2, n+1):
    print(milestone[i])

Solution (Python):
from collections import deque


def wfs(start):
    reached = [None] + [0] * N
    exit = [None] + [-1] * N
    q = deque()

    q.append(start)
    reached[start] = 1
    while q:
        p = q.popleft()
        for r in V[p]:
            if reached[r]:
                continue
            reached[r] = 1
            exit[r] = p
            q.append(r)

    return exit


N, M = map(int, input().split())
V = [None] + [[] for _ in range(N)]
for _ in range(M):
    A, B = list(map(int, input().split()))
    V[A].append(B)
    V[B].append(A)

exit = wfs(1)[2:]
if min(exit) == -1:
    print('No')
else:
    print('Yes')
    for e in exit:
        print(e)

Solution (Python):
import sys
from collections import deque

input = sys.stdin.readline


def bfs(G, v, check):
    queue = deque([v])
    while queue:
        v = queue.popleft()
        for u in G[v]:
            if check[u] != -1:
                continue
            check[u] = v + 1
            queue.append(u)


def main():
    N, M = map(int, input().split())
    G = [[] for _ in range(N)]
    for _ in range(M):
        A, B = map(int, input().split())
        A -= 1
        B -= 1
        G[A].append(B)
        G[B].append(A)

    check = [-1] * N
    check[0] = 0
    bfs(G, 0, check)

    print("Yes")
    print(*check[1:], sep="\n")


if __name__ == "__main__":
    main()

Solution (Python):
from collections import deque

n, m = (int(x) for x in input().split())
list_load=[[0] for i in range(n)]
for i in range(m):
    a, b = (int(x) for x in input().split())
    list_load[a-1].append(b)
    list_load[b-1].append(a)
list_ans=[0]*n

que=deque()
que.append(1)
while que:
    now = que.pop()
    for i in list_load[now-1]:
        if i!=0:
            if list_ans[i-1]==0:
                list_ans[i-1]=now
                que.appendleft(i)
bool = True
for i in range(1,n):
    if list_ans[i]==0:
        bool=False
if bool:
    print("Yes")
    for i in range(1,n):
        print(list_ans[i])
else:
    print("No")

Solution (Python):
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor, cos, radians, pi, sin
from operator import mul
from functools import reduce
from operator import mul


sys.setrecursionlimit(2147483647)
INF = 10 ** 13
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def I(): return int(sys.stdin.buffer.readline())
def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()
def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]


n, m = LI()
G = [[] for _ in range(n)]
for _ in range(m):
    a, b = LI()
    G[a - 1] += [b - 1]
    G[b - 1] += [a - 1]

D = [-1] * n
D[0] = 0
q = deque([0])
while q:
    u = q.popleft()
    for v in G[u]:
        if D[v] == -1:
            D[v] = D[u] + 1
            q += [v]

print('Yes')
for i in range(1, n):
    ret = INF
    for j in G[i]:
        if D[j] < ret:
            ret = D[j]
            ans = j
    print(ans + 1)

Solution (Python):
from collections import deque
n,m=map(int,input().split())
g=[[] for i in range(n)]
INF=1001001001
par=[INF for i in range(n)]
par[0]=0
for i in range(m):
  s,t=map(int,input().split())
  g[s-1].append(t-1)
  g[t-1].append(s-1)

q=deque([])
q.append(0)
while q:
  now = q.popleft()
  for i in g[now]:
    if par[i]==INF:
      par[i]=now
      q.append(i)

print("Yes")
for i in range(1,n):
  print(par[i]+1)

Solution (Python):
import sys
import math
import numpy as np
from collections import Counter, defaultdict, deque

input = sys.stdin.readline
sys.setrecursionlimit(10 ** 6)


def S():
    return input().rstrip()


def I():
    return int(input())


def MI():
    return map(int, input().split())


inf = float("inf")

n, m = MI()
way = defaultdict(set)
for _ in range(m):
    a, b = MI()
    way[a].add(b)
    way[b].add(a)

passed = [0] * (n + 1)
q = set([1])
while q:
    qq = set()
    for room in q:
        for next in way[room]:
            if not passed[next]:
                passed[next] = room
                qq.add(next)
    q = qq

if all(passed[2:]):
    print("Yes")
    for p in passed[2:]:
        print(p)
else:
    print("No")

Solution (Python):
N,M = map(int,input().split())
AB = [list(map(int,input().split())) for i in range(M)]
from collections import deque
from collections import defaultdict


ans = [0]*N

new_AB = []
for ab in AB:
    new_AB.append([ab[0],ab[1]])
    new_AB.append([ab[1],ab[0]])


adj = defaultdict(list)

for ab in new_AB:
    adj[ab[0]].append(ab[1])

q = deque()
q.append(1)



while len(q) > 0:
    
    node = q.popleft()
    

    for next_node in adj[node]:
        if ans[next_node-1] != 0:
            continue
        ans[next_node-1] = node
        q.append(next_node)



print("Yes")
for an in ans[1:]:
    print(an)

Solution (Python):
import sys
import heapq
import re
from itertools import permutations
from bisect import bisect_left, bisect_right
from collections import Counter, deque
from math import factorial, sqrt, ceil, gcd
from functools import lru_cache, reduce
INF = 1 << 60
MOD = 1000000007
sys.setrecursionlimit(10 ** 7)


class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


def dijkstra_heap(s, edge, n):
    
    d = [10**20] * n
    used = [True] * n 
    d[s] = 0
    used[s] = False
    edgelist = []
    for a,b in edge[s]:
        heapq.heappush(edgelist,a*(10**6)+b)
    while len(edgelist):
        minedge = heapq.heappop(edgelist)
        
        if not used[minedge%(10**6)]:
            continue
        v = minedge%(10**6)
        d[v] = minedge//(10**6)
        used[v] = False
        for e in edge[v]:
            if used[e[1]]:
                heapq.heappush(edgelist,(e[0]+d[v])*(10**6)+e[1])
    return d


def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr


def lcm(x, y):
    return (x * y) // gcd(x, y)


def lcm_list(numbers):
    return reduce(lcm, numbers, 1)


def gcd_list(numbers):
    return reduce(gcd, numbers)


def is_prime(n):
    if n <= 1:
        return False
    p = 2
    while True:
        if p ** 2 > n:
            break
        if n % p == 0:
            return False
        p += 1
    return True



def eratosthenes(limit):
    A = [i for i in range(2, limit+1)]
    P = []

    while True:
        prime = min(A)
        
        if prime > sqrt(limit):
            break
            
        P.append(prime)
            
        i = 0
        while i < len(A):
            if A[i] % prime == 0:
                A.pop(i)
                continue
            i += 1
            
    for a in A:
        P.append(a)
            
    return P


def permutation_with_duplicates(L):

    if L == []:
        return [[]]

    else:
        ret = []

        
        S = sorted(set(L))

        for i in S:

            data = L[:]
            data.remove(i)

            for j in permutation_with_duplicates(data):
                ret.append([i] + j)

        return ret



n, m = map(int, input().split())


edge = [[] for i in range(n)]
for i in range(m):
    a, b = map(int, input().split())
    edge[a - 1].append([1, b - 1])
    edge[b - 1].append([1, a - 1])

cost = dijkstra_heap(0, edge, n)

print("Yes")
for i in range(1, n):
    minimum = INF
    ans = None
    for j in edge[i]:
        if cost[j[1]] < minimum:
            minimum = cost[j[1]]
            ans = j[1]
    print(ans + 1)

Solution (Python):
from collections import defaultdict
import queue
def dfs(i):
    global count
    if count >= N or ans[i] != 0:
        return
    
    for ii in A2B[i]:
        dfs(ii)
N, M = map(int, input().split())
A2B = defaultdict(list)
ans = [0 for i in range(N+1)] 

for m in range(M):
    a, b = map(int, input().split())
    A2B[a] += [b]
    A2B[b] += [a]
count = 0
q = queue.Queue()
q.put((1, 1))
while count < N:
    t, f = q.get()
    if ans[t] != 0:
        continue
    count += 1
    ans[t] = f
    for x in A2B[t]:
        q.put((x, t))
print('Yes')
for i in range(2, N+1):
    print(ans[i])

Solution (Python):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

from collections import deque 
def main():
    N, M = map(int, readline().split())
    to = [[]  for _ in range(N)]
    for _ in range(M):
        a, b = map(int, readline().split())
        to[a-1].append(b-1)
        to[b-1].append(a-1) 

    dq = deque()
    dq.append(0)
    done = [0 for _ in range(N)]
    done[0] = 1
    ans = [0 for _ in range(N)]
    while len(dq) > 0:
        v = dq.popleft()
        for nx in to[v]:
            if done[nx]:
                continue
            ans[nx] = v
            done[nx] = 1
            dq.append(nx) 
    print('Yes')
    for i in ans[1:]:
        print(i+1)
if __name__ == '__main__':
    main()

Solution (Python):
n, m = map(int, input().split())

g = [[] for _ in range(n)]
for _ in range(m):
   a, b = map(int, input().split())
   g[a-1].append(b-1)
   g[b-1].append(a-1)

from collections import deque

ans = [-1] * n
def bfs(u):
   queue = deque([u])
   d = [None] * n
   d[u] = 0
   while queue:
      v = queue.popleft()
      for i in g[v]:
         if d[i] is None:
            d[i] = d[v] + 1
            queue.append(i)
            ans[i] = v + 1

   return d

d = bfs(0)
ans.pop(0)
if -1 in ans:
   print('No')
else:
   print('Yes')
   for x in ans:
      print(x)

Solution (Python):
from collections import deque
n,m = map(int,input().split())
G = [[] for _ in range(n)]
for _ in range(m):
    a,b = map(int,input().split())
    a -= 1
    b -= 1
    G[a].append(b)
    G[b].append(a)

seen = [False]*n
ans = [0]*n
Q = deque()
def f(s):
    Q.append(s)
    seen[s] = True
    while Q:
        now = Q.popleft()
        for nxt in G[now]:
            if seen[nxt]: continue
            ans[nxt] = now+1
            Q.append(nxt)
            seen[nxt] = True
f(0)
print("Yes")
for i in range(1,n): print(ans[i])

Solution (Python):
import sys
import copy
import math
import bisect
import pprint
import bisect
from functools import reduce
from copy import deepcopy
from collections import deque
from decimal import *

import numpy as np

import math

def rootCheck(checkList):
    nextList=[]
    for i in checkList:
        for j in root[i]:
            if hint[j] == -1:
                hint[j] = i
                nextList.append(j)
    if len(nextList) >0:
        rootCheck(nextList)



if __name__ == '__main__':
    sys.setrecursionlimit(10 ** 6)
    n, m = map(int, input().split())
    root = {}
    for i in range(m):
        b, c = map(int, input().split())
        if b-1 in root:
            root[b-1].append(c-1)
        else:
            root[b-1]=[c-1]
        if c-1 in root:
            root[c-1].append(b-1)
        else:
            root[c-1]=[b-1]
    hint =[-1]*n

    for i in root[0]:
        if hint[i] == -1:
            hint[i] = 0


    rootCheck(root[0])

    if -1 in hint:
        print("No")
    else:
        print("Yes")
        for i in hint[1:]:
            print(i+1)

Solution (Python):

import copy

class Node():
    def __init__(self, index):
        self.index = index
        self.connect = []
        self.michi = None
    
    def add_edge(self, node):
        self.connect.append(node)
    
    def show_connect_node_index(self):
        return [node.index for node in self.connect]
    
    def add_michisirube(self, index):
        self.michi = index


N, M = map(int, input().split())
node_list = [Node(i) for i in range(1,N+1)]

for m in range(M):
    A_m, B_m = map(int, input().split())
    node_list[A_m-1].add_edge(node_list[B_m-1])
    node_list[B_m-1].add_edge(node_list[A_m-1])


tansaku_node = [node_list[0]]
while tansaku_node != []:
    new_tansaku_node = []
    for node in tansaku_node:
        for child_node in node.connect:
            if child_node.michi == None:
                child_node.michi = node.index
                new_tansaku_node.append(child_node)
    tansaku_node = new_tansaku_node

print('Yes')
for n in range(1,N):
    print(node_list[n].michi)

Solution (Python):
n,m = map(int,input().split())
g = [[] for i in range(n)]
for i in range(m):
    a,b = map(int,input().split())
    a -= 1
    b -= 1
    g[a].append(b)
    g[b].append(a)
from collections import deque
d = deque([[0,0]]) 
ans = [-1 for i in range(n)]
kak = [-100 for i in range(n)]
while d:
    u,v = d.popleft()
    if ans[u] == -1:
        ans[u] = v
    for j in g[u]:
        if ans[j] == -1 and kak[j] == -100:
            kak[j] = 0
            d.append([j,u])
        else:
            continue
print('Yes')
for i in range(1,n):
    print(ans[i]+1)

Solution (Python):
def main():
    from collections import deque
    n, m, *ab = map(int, open(0).read().split())
    l = [[] for _ in range(n+1)]
    for i, j in zip(*[iter(ab)] * 2):
        l[i].append(j)
        l[j].append(i)

    ll = [0 for _ in range(n+1)]
    vis = [False for _ in range(n+1)]
    que = deque()
    que.append(1)
    vis[1] = True
    while que:
        now = que.popleft()
        nx = l[now]
        for i in nx:
            if vis[i]:
                continue
            vis[i] = True
            ll[i] = now
            que.append(i)
    if all(vis[1:]):
        print("Yes")
        s = "\n".join(map(str, ll[2:]))
        print(s)
    else:
        print("No")



if __name__ == '__main__':
    main()

Solution (Python):
import collections

n,m=map(int,input().split())
g=[[] for _ in range(n+1)]
for _ in range(m):
  a,b=map(int,input().split())
  g[a].append(b)
  g[b].append(a)
q=collections.deque()
q.append(1)
check=[0]*(n+1)
check[1]=1
ans=[0]*(n+1)
while len(q)!=0:
  v=q.popleft()
  for u in g[v]:
    if check[u]==0:
      check[u]=1
      ans[u]=v
      q.append(u)
print('Yes')
for i in range(2,n+1):
  print(ans[i])

Solution (Python):
import queue

n, m = map(int, input().split())
maze = [[] for _ in range(n)]
for i in range(m):
    a, b = map(int, input().split())
    maze[a-1].append(b-1)
    maze[b-1].append(a-1)

ans = [-1 for _ in range(n)]
ans[0] = 0
q = queue.Queue()
q.put(0)
while not q.empty():
    start = q.get()
    for end in maze[start]:
        if ans[end] == -1:
            q.put(end)
            ans[end] = start

if -1 in ans[1:]:
    print('No')
else:
    print('Yes')
    for i in range(1,n):
        print(ans[i]+1)

Solution (Python):
from collections import defaultdict
from queue import Queue
n,m = map(int,input().split())
graph = defaultdict(list)
for _ in range(m):
	a,b = map(int,input().split())
	graph[a].append(b)
	graph[b].append(a)

visited = [0]*(n+1)

visited[1] = 1
q = Queue()
q.put(1)
while not q.empty():
	x = q.get()
	rooms = graph[x]
	for r in rooms:
		if visited[r] == 0:
			visited[r] = x
			q.put(r)

possible = True
for i in range(2,n+1):
	if visited[i] == 0:
		possible = False
		break
if possible:
	print("Yes")
	for i in range(2,n+1):
		print(visited[i])
else:
	print("No")

Solution (Python):
from collections import deque
n,m=map(int,input().split())
maze=[[]for i in range(n)]
for i in range(m):
    r,l=map(int,input().split())
    maze[r-1].append(l-1)
    maze[l-1].append(r-1)

stamp=[-1]*n
queue=deque([0])
while queue:
    d=queue.popleft()
    for i in maze[d]:
        if stamp[i]==-1:
            stamp[i]=d
            queue.append(i)

print("Yes")
for i in range(1,n,1):
    print(stamp[i]+1)

Solution (Python):
from heapq import heappush, heappop
INF = 10**10

def dijkstra(n, G, s):
  dist = [INF] * n 
  que = [(0, s)]   
  dist[s] = 0
  last = [[] for _ in range(n)]
    
  while que:
    c, v = heappop(que)
    if dist[v] < c:
      continue
    for t, cost in G[v]: 
      if dist[v] + cost < dist[t]:
        dist[t] = dist[v] + cost
        heappush(que, (dist[t], t))                
        last[t].append(v)                        

  return dist,last

n,m = map(int,input().split())
G = [[]*n for _ in range(n)]
for i in range(m):
  a,b = map(int,input().split())
  G[a-1].append((b-1,1))
  G[b-1].append((a-1,1))
  
ans,last = dijkstra(n,G,0)

if max(ans) > m:
  print('No')
else:
  print('Yes')
  for i in range(1,n):    
    print(last[i][-1]+1)
    pass

Solution (Python):
from collections import deque

N, M = map(int, input().split())

list_road = [[] for _ in range(N)]
for _ in range(M):
    A, B = map(int, input().split())
    list_road[A-1].append(B-1)
    list_road[B-1].append(A-1)

list_step = [-1] * N
list_step[0] = 0
queue = deque([0])
while len(queue) > 0:
    parent = queue.popleft()
    for i in range(len(list_road[parent])):
        tmp = list_road[parent][i]
        if list_step[tmp] == -1:
            list_step[tmp] = parent
            queue.append(tmp)

if -1 in list_step:
    print('No')
else:
    print('Yes')
    for i in range(1, N):
        print(list_step[i]+1)

Solution (Python):
import sys
input = lambda: sys.stdin.readline().rstrip()
from collections import deque

N, M = map(int, input().split())

edges_list = [[] for _ in range(N)]
seen_list = [-1] * N

for i in range(M):
    A, B = map(int, input().split())
    A -= 1
    B -= 1
    edges_list[A].append(B)
    edges_list[B].append(A)

queue = deque([0])
seen_list[0] = 0

while queue:
    current = queue.popleft()
    for n in edges_list[current]:
        if seen_list[n] == -1:
            seen_list[n] = current
            queue.append(n)

if -1 in seen_list:
    print("No")
else:
    print("Yes")
    for i in range(len(seen_list) - 1):
        print(seen_list[i+1] + 1)

Solution (Python):
from collections import deque

N, M = map(int, input().split())
con = [[] for _ in range(N)]
for i in range(M):
    A, B = map(int, input().split())
    con[A-1].append(B-1)
    con[B-1].append(A-1)
    
d = deque()
houmon = [False] * N
ans = [0] * (N-1)

houmon[0] = True
d.append(0)
while d:

    room = d.popleft()


    
    for next_room in con[room]:
        if not houmon[next_room]:
            ans[next_room-1] = room+1
            d.append(next_room)
            houmon[next_room] = True
    
print('Yes\n' + '\n'.join(map(str, ans)))

Solution (Python):
import heapq

N, M = list(map(int, input().split()))
path = [[] for _ in range(N + 1)]
for _ in range(M):
  A, B = list(map(int, input().split()))
  path[A].append(B)
  path[B].append(A)



hq = [(0, 0, 1)]

mark = [None] * (N + 1)

while hq:
  cost, prev, node = heapq.heappop(hq)
  
  if not mark[node]:
    mark[node] = prev
    for nxt in path[node]:
      heapq.heappush(hq, (cost + 1, node, nxt))

if all(mark[2:]):
  print('Yes')
  for m in mark[2:]:
    print(m)
else:
  print('No')

Solution (Python):
from collections import deque
import heapq
class Graph:
    edges = {}

    def append_edge(self, sv, ev, weight = 1):
        if sv in self.edges:
            self.edges[sv].append((ev, weight))
        else:
            self.edges[sv] = [(ev, weight)]

    def bfs(self, sv, n):
        dist = [-1]*len(self.edges.keys())
        q = deque([])   
        q.append(sv)
        dist[sv] = 0
        connect_vtxs = []
        ans = [-1] * n
        ans[0] = -1
        while len(q) > 0:
            p = q.popleft()     
            connect_vtxs.append(p)
            for (ev, w) in self.edges[p]:
                if ans[ev] == -1:
                    ans[ev] = p
                if dist[ev] != -1:
                    continue
                q.append(ev)    
                dist[ev] = dist[p] + 1
        return ans


N, M = list(map(int, input().split()))
ab = [list(map(int, input().split())) for i in range(M)]

for i in range(len(ab)):
    ab[i][0] -= 1
    ab[i][1] -= 1

g = Graph()
for i in range(M):
    s = ab[i][0]
    t = ab[i][1]
    g.append_edge(s, t)
    g.append_edge(t, s)

ans = g.bfs(0, N)
ans = ans[1:]

if -1 in ans:
    print("No")
else:
    print("Yes")
    for i in range(N-1):
        print(ans[i]+1)

Solution (Python):
N,M=map(int,input().split())

S=[[] for _ in range(N)]
for _ in range(M):
    a,b=map(int,input().split())
    S[a-1].append(b-1)
    S[b-1].append(a-1)

L=[-1]*N
L[0]=0
tmp=[0]
while tmp:
    T0=tmp.pop(0)
    
    for j in S[T0]:
        if L[j]==-1:
            L[j]=T0
            tmp.append(j)

label=True
for j in L:
    if L==-1:
        label=False
if label:
    print('Yes')
    for j in L[1:]:
        print(j+1)
else:
    print('No')

Solution (Python):
n,m = map(int,input().split())
ls = [[] for i in range(n+1)]

for _ in range(m):
  p,q = map(int,input().split())
  ls[p].append(q)
  ls[q].append(p)
ans = [None]*(n+1)

cur = 1
que = [1]
count = 1
while que:
  cur = que.pop(0)
  for v in ls[cur]:
    if ans[v] == None:
      ans[v] = cur
      que.append(v)
      

print("Yes")
for s in ans[2:]:
  print(s)

Solution (Python):
n,m = map(int,input().split())
a = [0 for _ in range(m)]
b = [0 for _ in range(m)]

for i in range(m):
    a[i],b[i] = map(int,input().split())
    a[i] -= 1
    b[i] -= 1

ans = [-1 for _ in range(n-1)]
looked = [1 for _ in range(n)]
queue = [0]
looked[0] = 0
can = [[] for _ in range(n)]

for i in range(m):
    can[a[i]].append(b[i])
    can[b[i]].append(a[i])

while(len(queue)):
    now = queue.pop(0)
    for i in can[now]:
        if looked[i]:
            queue.append(i)
            looked[i] = 0
            ans[i-1] = now+1
for i in ans:
    if ans == -1:
        print("No")
        exit
print("Yes")
for i in ans:
    print(i)

Solution (Python):
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]





from collections import deque
    
N, M = mi()

rel = [[] for _ in range(N)]

mark = [-1]*N
flag = [0]*N
mark[0] = 0
l = deque([0])
'''
def dfs(s):
    print(mark)
    if rel[s]:
        for num in rel[s]:
            if mark[num] == -1:
                mark[num] = s
        for num in rel[s]:
            if rel[num]:
                dfs(num)   
'''
for i in range(M):
    s, t = mi()
    s -= 1
    t -= 1
    rel[s].append(t)
    rel[t].append(s)


flag[0] = 1
while l != deque([]):
    a = l.popleft()
    for num in rel[a]:
        if not flag[num]:
            mark[num] = a
            flag[num] = 1
            l.append(num)

if sum(flag) != N:
    print('No')
    exit()
print('Yes')
for i in range(1, N):
    print(mark[i]+1)

Solution (Python):



def main():
    import sys
    input = sys.stdin.readline
    sys.setrecursionlimit(10**6)
    

    def dump(*args):
        sys.stderr.write(str(args))
    from collections import deque
    INF = 10**12

    import heapq
    import sys

    input = sys.stdin.readline

    def dijkstra_heap(s, edge, n):
        
        d = [INF] * n
        used = [True] * n  
        d[s] = 0
        used[s] = False
        edgelist = []
        frm = [-1]*n
        for a, b in edge[s]:
            heapq.heappush(edgelist, (a*(10**6)+b, -1))
        while len(edgelist):
            minedge = heapq.heappop(edgelist)
            froom = minedge[1]
            minedge = minedge[0]
            
            if not used[minedge % (10**6)]:
                continue
            v = minedge % (10**6)
            d[v] = minedge // (10 ** 6)
            frm[v] = froom
            used[v] = False
            for e in edge[v]:
                if used[e[1]]:
                    heapq.heappush(edgelist, ((e[0]+d[v])*(10**6)+e[1], v))
        return (d, frm)

    n, m = map(int, input().split())
    edges = [list() for _ in range(n)]
    for _ in range(m):
        a, b = map(int, input().split())
        edges[a - 1].append((1, b - 1))
        edges[b - 1].append((1, a - 1))

    dist = dijkstra_heap(0, edges, n)
    
   
    
    if INF in dist[0]:
        print('No')
        exit(0)
    print('Yes')
    for i in dist[1][1:]:
        print(i+1 if i+1 != 0 else 1)


if __name__ == '__main__':
    main()

Solution (Python):
from collections import deque
N,M = list(map(int, input().split()))

E = {}
for i in range(N):
  E[i] = set()
  
for i in range(M):
  a,b = list(map(int, input().split()))
  a,b = a-1, b-1
  E[a].add(b)
  E[b].add(a)
  
visited = [False] * N
will_search = [False] * N
q = deque()
q.append(0)
ans = [0] * N
while len(q) >0:
  now = q.popleft()
  visited[now] = True
  for x in E[now]:
    if visited[x] or will_search[x]:
      continue
    will_search[x] = True
    ans[x] = now
    q.append(x)
    
if len(ans) < N:
  print('No')
else:
  print('Yes')
  for a in ans[1:]:
    print(a+1)

Solution (Python):
from collections import deque

n, m = map(int, input().split())
g = [[] for _ in range(n)]
for _ in range(m):
    a, b = map(lambda x: int(x)-1, input().split())
    g[a].append(b)
    g[b].append(a)

visited = [False] * n
q = deque()
q.append((0, -1))
ans = [0] * n

while q:
    v, pv = q.popleft()
    ans[v] = pv+1
    for nv in g[v]:
        if visited[nv]: continue
        visited[nv] = True
        q.append((nv, v))

print("Yes")
print(*ans[1:], sep="\n")

Solution (Python):
from collections import deque

n, m = map(int, input().split())

g = [[] for _ in range(n)]
for i in range(m):
    a, b = map(int, input().split())

    g[a-1].append(b-1)
    g[b-1].append(a-1)

d = [-1] * n
d[0] = 0
b = [[] for _ in range(n)]
q = deque([0])
while q:
    v = q.popleft()
    for e in g[v]:
        if d[e] == -1:
            d[e] = d[v] + 1
            b[e].append(v)
            q.append(e)

if -1 in d:
    print("No")
else:
    print("Yes")
    for i in range(1, n):
        print(b[i][0]+1)

Solution (Python):
from collections import deque
N, M = map(int, input().split())
graph = [[] for _ in range(N)]
for i in range(M):
    a, b = map(lambda x: int(x)-1, input().split())
    graph[a].append(b)
    graph[b].append(a)


queue = deque()
seen = [-1] * N
steps = [-1] * N
steps[0] = 0
parents = [-1] * N
queue.append(0)
while queue:
    node = queue.popleft()

    seen[node] = 1
    
    for next in graph[node]:
        if seen[next] > -1:
            continue
        
        queue.append(next)
        seen[next] = 1
        steps[next] = steps[node] + 1
        parents[next] = node

print("Yes")
for a in parents[1:]:
    print(a+1)