Buggy python submission (verdict: Time Limit Exceeded):
from collections import deque
def main():
    n,m=map(int,input().split())
    root=[[0 for i in range(n)] for i in range(n)]
    for i in range(m):
        a,b=map(int,input().split())
        root[a-1][b-1]=1
        root[b-1][a-1]=1
    dict={}
    for i in range(n):
        dict[i]=-1

    start=0
    check=[False]*n
    toVis=deque()
    check[start]=True
    for i in range(len(root[0])):
        if root[0][i]==1:
            toVis.append(i)
            dict[i]=start
        #   print(i,":",start)
            check[i]=True
    while len(toVis)>0:
        now=toVis.popleft()
        #print(now)
        check[now]=True
        for i in range(n):
            if root[now][i]==1 and check[i]==False:
                toVis.append(i)
                dict[i]=now
            # print(i,":",now)
                check[i]=True
    #print(dict)  
    for i in range(1,n):
        if dict[i]==-1:
            print("No")
            return 0
    print("Yes")
    for i in range(1,n):
        print(dict[i]+1)         


if __name__=="__main__":
    main()

Fixed submission:
from collections import deque
def main():
    n,m=map(int,input().split())
    root=[[] for i in range(n)]
    for i in range(m):
        a,b=map(int,input().split())
        root[a-1].append(b-1)
        root[b-1].append(a-1)
    dict={}
    for i in range(n):
        dict[i]=-1

    start=0
    check=[False]*n
    toVis=deque()
    check[start]=True
    for v in root[start]:
        toVis.append(v)
        dict[v]=start
    #   print(i,":",start)
        check[v]=True
    while len(toVis)>0:
        now=toVis.popleft()
        #print(now)
        check[now]=True
        for v in root[now]:
            if check[v]==False:
                toVis.append(v)
                dict[v]=now
            # print(i,":",now)
                check[v]=True
    #print(dict)  
    for i in range(1,n):
        if dict[i]==-1:
            print("No")
            return 0
    print("Yes")
    for i in range(1,n):
        print(dict[i]+1)         


if __name__=="__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
from collections import deque
def main():
    n,m=map(int,input().split())
    root=[[0 for i in range(n)] for i in range(n)]
    for i in range(m):
        a,b=map(int,input().split())
        root[a-1][b-1]=1
        root[b-1][a-1]=1
    min=[-1 for i in range(n)]
    min[0]=2
    dict={}
    for i in range(n):
        dict[i]=-1

    start=0
    check=[False]*n
    toVis=deque()
    check[start]=True
    for i in range(len(root[0])):
        if root[0][i]==1:
            toVis.append(i)
            dict[i]=start
        #   print(i,":",start)
            check[i]=True
    while len(toVis)>0:
        now=toVis.popleft()
        #print(now)
        check[now]=True
        for i in range(n):
            if root[now][i]==1 and check[i]==False:
                toVis.append(i)
                dict[i]=now
            # print(i,":",now)
                check[i]=True
    #print(dict)  
    for i in range(1,n):
        if dict[i]==-1:
            print("No")
            return 0
    print("Yes")
    for i in range(1,n):
        print(dict[i]+1)         


if __name__=="__main__":
    main()

Fixed submission:
from collections import deque
def main():
    n,m=map(int,input().split())
    root=[[] for i in range(n)]
    for i in range(m):
        a,b=map(int,input().split())
        root[a-1].append(b-1)
        root[b-1].append(a-1)
    dict={}
    for i in range(n):
        dict[i]=-1

    start=0
    check=[False]*n
    toVis=deque()
    check[start]=True
    for v in root[start]:
        toVis.append(v)
        dict[v]=start
    #   print(i,":",start)
        check[v]=True
    while len(toVis)>0:
        now=toVis.popleft()
        #print(now)
        check[now]=True
        for v in root[now]:
            if check[v]==False:
                toVis.append(v)
                dict[v]=now
            # print(i,":",now)
                check[v]=True
    #print(dict)  
    for i in range(1,n):
        if dict[i]==-1:
            print("No")
            return 0
    print("Yes")
    for i in range(1,n):
        print(dict[i]+1)         


if __name__=="__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import queue
def main():
    n,m=map(int,input().split())
    root=[[0 for i in range(n)] for i in range(n)]
    for i in range(m):
        a,b=map(int,input().split())
        root[a-1][b-1]=1
        root[b-1][a-1]=1
    min=[-1 for i in range(n)]
    min[0]=2
    dict={}
    for i in range(n):
        dict[i]=-1

    start=0
    check=[False]*n
    toVis=queue.Queue()
    check[start]=True
    for i in range(len(root[0])):
        if root[0][i]==1:
            toVis.put(i)
            dict[i]=start
        #   print(i,":",start)
            check[i]=True
    while(toVis.empty()!=True):
        now=toVis.get()
        #print(now)
        check[now]=True
        for i in range(n):
            if root[now][i]==1 and check[i]==False:
                toVis.put(i)
                dict[i]=now
            # print(i,":",now)
                check[i]=True
    #print(dict)  
    for i in range(1,n):
        if dict[i]==-1:
            print("No")
            return 0
    print("Yes")
    for i in range(1,n):
        print(dict[i]+1)         


if __name__=="__main__":
    main()

Fixed submission:
from collections import deque
def main():
    n,m=map(int,input().split())
    root=[[] for i in range(n)]
    for i in range(m):
        a,b=map(int,input().split())
        root[a-1].append(b-1)
        root[b-1].append(a-1)
    dict={}
    for i in range(n):
        dict[i]=-1

    start=0
    check=[False]*n
    toVis=deque()
    check[start]=True
    for v in root[start]:
        toVis.append(v)
        dict[v]=start
    #   print(i,":",start)
        check[v]=True
    while len(toVis)>0:
        now=toVis.popleft()
        #print(now)
        check[now]=True
        for v in root[now]:
            if check[v]==False:
                toVis.append(v)
                dict[v]=now
            # print(i,":",now)
                check[v]=True
    #print(dict)  
    for i in range(1,n):
        if dict[i]==-1:
            print("No")
            return 0
    print("Yes")
    for i in range(1,n):
        print(dict[i]+1)         


if __name__=="__main__":
    main()