Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
import sys
#import copy


def xnxn(n=0, flag="v"):
    """
    args:
        int n: a number of lows to read
    example:
        input   1
        retrun  1

        input   1 2 3
        return  [1,2,3]
        input   1 2 3
                4 
        return  [[1,2,3],
                [4]]
    """
    if n == 0:
        temp = list(map(int, input().split()))
        if len(temp) == 1:
            if flag == "l":
                return temp
            else:
                return temp[0]
        elif len(temp) > 1:
            return temp
    else:
        temp = [list(map(int, input().split())) for _ in range(n)]
        return temp


def sp_xnxn(n=0):
    """
    args:
        int n: a number of lows to read
    example
        input   1
        retrun  [1]

        input   123
        return  [1,2,3]

        input   123
                4 
        return  [[1,2,3],
                [4]]
    """
    if n == 0:
        return [int(k) for k in xsxs()]
    else:
        return [[int(k) for k in xsxs()] for _ in range(n)]


def xsxs(n=0):
    """
    args:
        int n: a number of lows to read 
    example:
        input   AA
        retrun  AA

        input   A BBB CC
        return  ["A","BBB","CC"]

        input   A BB CCC
                D
        return  [["A","BBB","CC"],
                ["D"]]
    """
    if n == 0:
        temp = list(input().split())
        if len(temp) == 1:
            return temp[0]
        elif len(temp) > 1:
            return temp
    else:
        return [list(input().split()) for _ in range(n)]


def sp_xsxs(n=0):
    """
    args:
        int n: a number of lows to read 
        example:
            input   A
            retrun  ["A"]

            input   ABC
            return  ["A","B","C"]

            input   ABC
                    D
            return  [["A","B","C"],
                    ["D"]]
    """
    if n == 0:
        return [s for s in xsxs()]
    else:
        return [[s for s in xsxs()] for _ in range(n)]


n, m = xnxn()
a = xnxn(m)

graph = [[] for _ in range(n+1)]
for g in a:
    graph[g[0]].append(g[1])
    graph[g[1]].append(g[0])

# print(graph)

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


if rout != [0]*(n+1):
    print("Yes")
    for i in rout[2:]:
        print(i)
else:
    print("No")


Fixed submission:
#import copy
from collections import deque


def xnxn(n=0, flag="v"):
    """
    args:
        int n: a number of lows to read
    example:
        input   1
        retrun  1

        input   1 2 3
        return  [1,2,3]
        input   1 2 3
                4 
        return  [[1,2,3],
                [4]]
    """
    if n == 0:
        temp = list(map(int, input().split()))
        if len(temp) == 1:
            if flag == "l":
                return temp
            else:
                return temp[0]
        elif len(temp) > 1:
            return temp
    else:
        temp = [list(map(int, input().split())) for _ in range(n)]
        return temp


n, m = xnxn()
a = xnxn(m)

graph = [[] for _ in range(n+1)]
for g in a:
    graph[g[0]].append(g[1])
    graph[g[1]].append(g[0])

# print(graph)

d = deque([1])
rout = [0]*(n+1)
while d != deque([]):
    pos = d.popleft()
    for i in graph[pos]:
        if rout[i] == 0:
            rout[i] = pos
            d.append(i)


if rout != [0]*(n+1):
    print("Yes")
    for i in rout[2:]:
        print(i)
else:
    print("No")