Buggy python submission (verdict: Runtime Error):
from collections import Counter 
from collections import defaultdict
from collections import deque
from functools import reduce
import math
import itertools
import heapq
import numpy as np
import sys
sys.setrecursionlimit(10**6)

#n=int(input())
#n,m=list(map(int,input().split()))
#a=list(map(int,input().split()))
ceil=lambda x,y: (x+y-1)//y
input_list = lambda : list(map(int,input().split()))



#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node):
    check=[False for _ in range(n)]
    check[s]=True
    queue=[n for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    last_ind=1
    while last_ind<n:

        
        if now>=n or queue[now]==n:
            return []

        for i in node[queue[now]]:
            edge=i[0]
            
            ind=i[1]
            if check[edge]:
                continue

            queue[last_ind]=edge
            last_ind+=1
            #check[edge]=True
            
            ans[edge]=queue[now]
            check[edge]=True
        now+=1
        print(queue)
        print(last_ind)
        print()
    return ans



n,m=input_list()
node=[[] for _ in range(n)]
for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append([v,i])
    node[v].append([u,i])

#print(np.array(node))

ans=bfs(0,n,node)
if len(ans)==0:
    print("No")
    exit()

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








Fixed submission:
input_list = lambda : list(map(int,input().split()))


#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node):
    c=[-1 for _ in range(n)]
    c[0]=0
    
    side_num_arr=list(map(lambda x :len(x),node))
    #print(l)
    queue=[-1 for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    last_ind=1
    while last_ind<n:
        
        if now>=n:
            return []
        c[queue[now]]=True
        if side_num_arr[queue[now]]<=0:
            now+=1
            continue
        for edge in node[queue[now]]:
            #edge=i[0]
            if side_num_arr[edge]<=0 or c[edge]==True:
                continue
            side_num_arr[edge]-=1
            
            queue[last_ind]=edge
            last_ind+=1
            c[edge]=True
            ans[edge]=queue[now]

        side_num_arr[queue[now]]=0
        now+=1
    return ans



n,m=input_list()
node=[[] for _ in range(n)]

for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append(v)
    node[v].append(u)

#print(np.array(node))

ans=bfs(0,n,node)
if len(ans)==0:
    print("No")
    exit()

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

Buggy python submission (verdict: Runtime Error):
from collections import Counter 
from collections import defaultdict
from collections import deque
from functools import reduce
import math
import itertools
import heapq
import numpy as np
import sys
sys.setrecursionlimit(10**6)

#n=int(input())
#n,m=list(map(int,input().split()))
#a=list(map(int,input().split()))
ceil=lambda x,y: (x+y-1)//y
input_list = lambda : list(map(int,input().split()))



#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node):
    check=[False for _ in range(n)]
    queue=[n for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    last_ind=1
    while last_ind<n:
        #全探索が終わらない場合
        if queue[now]==n:
            return []
        if check[queue[now]]:
            now+=1
            continue
        for i in node[queue[now]]:
            edge=i[0]
            
            ind=i[1]
            if check[edge]:
                continue

            queue[last_ind]=edge
            last_ind+=1
            #check[edge]=True
            
            ans[edge]=queue[now]
        check[queue[now]]=True
        now+=1
    return ans



n,m=input_list()
node=[[] for _ in range(n)]
for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append([v,i])
    node[v].append([u,i])

#print(np.array(node))

ans=bfs(0,n,node)
if len(ans)==0:
    print("No")
    exit()

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








Fixed submission:
input_list = lambda : list(map(int,input().split()))


#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node):
    c=[-1 for _ in range(n)]
    c[0]=0
    
    side_num_arr=list(map(lambda x :len(x),node))
    #print(l)
    queue=[-1 for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    last_ind=1
    while last_ind<n:
        
        if now>=n:
            return []
        c[queue[now]]=True
        if side_num_arr[queue[now]]<=0:
            now+=1
            continue
        for edge in node[queue[now]]:
            #edge=i[0]
            if side_num_arr[edge]<=0 or c[edge]==True:
                continue
            side_num_arr[edge]-=1
            
            queue[last_ind]=edge
            last_ind+=1
            c[edge]=True
            ans[edge]=queue[now]

        side_num_arr[queue[now]]=0
        now+=1
    return ans



n,m=input_list()
node=[[] for _ in range(n)]

for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append(v)
    node[v].append(u)

#print(np.array(node))

ans=bfs(0,n,node)
if len(ans)==0:
    print("No")
    exit()

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

Buggy python submission (verdict: Runtime Error):
from collections import Counter 
from collections import defaultdict
from collections import deque
from functools import reduce
import math
import itertools
import heapq
import numpy as np
import sys
sys.setrecursionlimit(10**6)

#n=int(input())
#n,m=list(map(int,input().split()))
#a=list(map(int,input().split()))
ceil=lambda x,y: (x+y-1)//y
input_list = lambda : list(map(int,input().split()))



#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node):
    check=[False for _ in range(n)]
    queue=[n for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    last_ind=1
    while last_ind<n:
        print(now)
        print(queue)
        print(check)
        print()
        #全探索が終わらない場合
        if queue[now]==n:
            return []
        if check[queue[now]]:
            now+=1
            continue
        for i in node[queue[now]]:
            edge=i[0]
            
            ind=i[1]
            if check[edge]:
                continue

            queue[last_ind]=edge
            last_ind+=1
            #check[edge]=True
            
            ans[edge]=queue[now]
        check[queue[now]]=True
        now+=1
    return ans



n,m=input_list()
node=[[] for _ in range(n)]
for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append([v,i])
    node[v].append([u,i])

#print(np.array(node))

ans=bfs(0,n,node)
if len(ans)==0:
    print("No")
    exit()

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








Fixed submission:
input_list = lambda : list(map(int,input().split()))


#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node):
    c=[-1 for _ in range(n)]
    c[0]=0
    
    side_num_arr=list(map(lambda x :len(x),node))
    #print(l)
    queue=[-1 for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    last_ind=1
    while last_ind<n:
        
        if now>=n:
            return []
        c[queue[now]]=True
        if side_num_arr[queue[now]]<=0:
            now+=1
            continue
        for edge in node[queue[now]]:
            #edge=i[0]
            if side_num_arr[edge]<=0 or c[edge]==True:
                continue
            side_num_arr[edge]-=1
            
            queue[last_ind]=edge
            last_ind+=1
            c[edge]=True
            ans[edge]=queue[now]

        side_num_arr[queue[now]]=0
        now+=1
    return ans



n,m=input_list()
node=[[] for _ in range(n)]

for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append(v)
    node[v].append(u)

#print(np.array(node))

ans=bfs(0,n,node)
if len(ans)==0:
    print("No")
    exit()

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

Buggy python submission (verdict: Runtime Error):
from collections import Counter 
from collections import defaultdict
from collections import deque
from functools import reduce
import math
import itertools
import heapq
import numpy as np
import sys
sys.setrecursionlimit(10**6)

#n=int(input())
#n,m=list(map(int,input().split()))
#a=list(map(int,input().split()))
ceil=lambda x,y: (x+y-1)//y
input_list = lambda : list(map(int,input().split()))



#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node):
    check=[False for _ in range(n)]
    queue=[-1 for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    last_ind=1
    while last_ind<n:
        
        if now>=n:
            return []
        if check[queue[now]]:
            now+=1
            continue
        for i in node[queue[now]]:
            edge=i[0]
            
            ind=i[1]
            if check[edge]:
                continue

            queue[last_ind]=edge
            last_ind+=1
            #check[edge]=True
            
            ans[edge]=queue[now]
        check[queue[now]]=True
        now+=1
    return ans



n,m=input_list()
node=[[] for _ in range(n)]
for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append([v,i])
    node[v].append([u,i])

#print(np.array(node))

ans=bfs(0,n,node)
if len(ans)==0:
    print("No")
    exit()

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








Fixed submission:
input_list = lambda : list(map(int,input().split()))


#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node):
    c=[-1 for _ in range(n)]
    c[0]=0
    
    side_num_arr=list(map(lambda x :len(x),node))
    #print(l)
    queue=[-1 for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    last_ind=1
    while last_ind<n:
        
        if now>=n:
            return []
        c[queue[now]]=True
        if side_num_arr[queue[now]]<=0:
            now+=1
            continue
        for edge in node[queue[now]]:
            #edge=i[0]
            if side_num_arr[edge]<=0 or c[edge]==True:
                continue
            side_num_arr[edge]-=1
            
            queue[last_ind]=edge
            last_ind+=1
            c[edge]=True
            ans[edge]=queue[now]

        side_num_arr[queue[now]]=0
        now+=1
    return ans



n,m=input_list()
node=[[] for _ in range(n)]

for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append(v)
    node[v].append(u)

#print(np.array(node))

ans=bfs(0,n,node)
if len(ans)==0:
    print("No")
    exit()

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

Buggy python submission (verdict: Runtime Error):
from collections import Counter 
from collections import defaultdict
from collections import deque
from functools import reduce
import math
import itertools
import heapq
import numpy as np
import sys
sys.setrecursionlimit(10**6)

#n=int(input())
#n,m=list(map(int,input().split()))
#a=list(map(int,input().split()))
ceil=lambda x,y: (x+y-1)//y
input_list = lambda : list(map(int,input().split()))



#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node):
    
    side_num_arr=list(map(lambda x :len(x),node))
    l=max(side_num_arr)
    #print(l)
    queue=[-1 for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    last_ind=1
    while last_ind<n:
        
        if now>=n:
            return []
        if side_num_arr[queue[now]]<=0:
            now+=1
            continue
        for i in node[queue[now]]:
            edge=i[0]
            
            ind=i[1]
            if side_num_arr[edge]<=0:
                continue
            side_num_arr[edge]-=1
            side_num_arr[queue[now]]-=1
            queue[last_ind]=edge
            last_ind+=1
            
            ans[edge]=queue[now]
        now+=1
    return ans



n,m=input_list()
node=[[] for _ in range(n)]
for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append([v,i])
    node[v].append([u,i])

ans=bfs(0,n,node)
if len(ans)==0:
    print("No")
    exit()

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








Fixed submission:
input_list = lambda : list(map(int,input().split()))


#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node):
    c=[-1 for _ in range(n)]
    c[0]=0
    
    side_num_arr=list(map(lambda x :len(x),node))
    #print(l)
    queue=[-1 for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    last_ind=1
    while last_ind<n:
        
        if now>=n:
            return []
        c[queue[now]]=True
        if side_num_arr[queue[now]]<=0:
            now+=1
            continue
        for edge in node[queue[now]]:
            #edge=i[0]
            if side_num_arr[edge]<=0 or c[edge]==True:
                continue
            side_num_arr[edge]-=1
            
            queue[last_ind]=edge
            last_ind+=1
            c[edge]=True
            ans[edge]=queue[now]

        side_num_arr[queue[now]]=0
        now+=1
    return ans



n,m=input_list()
node=[[] for _ in range(n)]

for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append(v)
    node[v].append(u)

#print(np.array(node))

ans=bfs(0,n,node)
if len(ans)==0:
    print("No")
    exit()

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

Buggy python submission (verdict: Time Limit Exceeded):
from collections import Counter 
from collections import defaultdict
from collections import deque
from functools import reduce
import math
import itertools
import heapq

#n=int(input())
#n,m=list(map(int,input().split()))
#a=list(map(int,input().split()))
ceil=lambda x,y: (x+y-1)//y
input_list = lambda : list(map(int,input().split()))


#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node,c):
    
    side_num_arr=list(map(lambda x :len(x),node))
    l=max(side_num_arr)
    #print(l)
    queue=[-1 for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    color_check=[[True for _ in range(l)] for _ in range(n)]
    color=[-1 for _ in range(n-1)]
    last_ind=1
    while last_ind<n:
        
        if now>=n:
            return []
        check[queue[now]]=True
        if side_num_arr[queue[now]]<=0:
            now+=1
            continue
        for i in node[queue[now]]:
            edge=i[0]
            
            ind=i[1]
            if side_num_arr[edge]<=0 or check[edge]==True:
                continue
            side_num_arr[edge]-=1
            side_num_arr[queue[now]]-=1
            queue[last_ind]=edge
            last_ind+=1
            check[edge]=True
            
            ans[edge]=queue[now]
            #color[ind]=search_color(queue[now],edge,color_check)
        now+=1
    return ans



n,m=input_list()
node=[[] for _ in range(n)]
for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append([v,i])
    node[v].append([u,i])

#print(np.array(node))
check=[-1 for _ in range(n)]
check[0]=0
ans=bfs(0,n,node,check)
if len(ans)==0:
    print("No")
    exit()

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








Fixed submission:
input_list = lambda : list(map(int,input().split()))


#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node):
    c=[-1 for _ in range(n)]
    c[0]=0
    
    side_num_arr=list(map(lambda x :len(x),node))
    #print(l)
    queue=[-1 for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    last_ind=1
    while last_ind<n:
        
        if now>=n:
            return []
        c[queue[now]]=True
        if side_num_arr[queue[now]]<=0:
            now+=1
            continue
        for edge in node[queue[now]]:
            #edge=i[0]
            if side_num_arr[edge]<=0 or c[edge]==True:
                continue
            side_num_arr[edge]-=1
            
            queue[last_ind]=edge
            last_ind+=1
            c[edge]=True
            ans[edge]=queue[now]

        side_num_arr[queue[now]]=0
        now+=1
    return ans



n,m=input_list()
node=[[] for _ in range(n)]

for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append(v)
    node[v].append(u)

#print(np.array(node))

ans=bfs(0,n,node)
if len(ans)==0:
    print("No")
    exit()

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

Buggy python submission (verdict: Time Limit Exceeded):
from collections import Counter 
from collections import defaultdict
from collections import deque
from functools import reduce
import math
import itertools
import heapq
import numpy as np
import sys
sys.setrecursionlimit(10**6)

#n=int(input())
#n,m=list(map(int,input().split()))
#a=list(map(int,input().split()))
ceil=lambda x,y: (x+y-1)//y
input_list = lambda : list(map(int,input().split()))



def search_color(edge,next_edge,color_check):
    ind=color_check[edge].index(True)
    color_check[edge][ind]=False
    color_check[next_edge][ind]=False
    return ind+1
#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node,c):
    
    side_num_arr=list(map(lambda x :len(x),node))
    l=max(side_num_arr)
    #print(l)
    queue=[-1 for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    color_check=[[True for _ in range(l)] for _ in range(n)]
    color=[-1 for _ in range(n-1)]
    last_ind=1
    while last_ind<n:
        
        if now>=n:
            return []
        check[queue[now]]=True
        if side_num_arr[queue[now]]<=0:
            now+=1
            continue
        for i in node[queue[now]]:
            edge=i[0]
            
            ind=i[1]
            if side_num_arr[edge]<=0 or check[edge]==True:
                continue
            side_num_arr[edge]-=1
            side_num_arr[queue[now]]-=1
            queue[last_ind]=edge
            last_ind+=1
            check[edge]=True
            
            ans[edge]=queue[now]
            #color[ind]=search_color(queue[now],edge,color_check)
        now+=1
    return ans



n,m=input_list()
node=[[] for _ in range(n)]
for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append([v,i])
    node[v].append([u,i])

#print(np.array(node))
check=[-1 for _ in range(n)]
check[0]=0
ans=bfs(0,n,node,check)
if len(ans)==0:
    print("No")
    exit()

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








Fixed submission:
input_list = lambda : list(map(int,input().split()))


#bfs内で処理すると使い回しが効かないのでsearch_color とか幅探索後の具体的な処理は別個にしたほうがいい
def bfs(s,n,node):
    c=[-1 for _ in range(n)]
    c[0]=0
    
    side_num_arr=list(map(lambda x :len(x),node))
    #print(l)
    queue=[-1 for _ in range(n)]
    now=0
    queue[now]=s
    ans=[-1 for _ in range(n)]
    ans[0]=[0]
    last_ind=1
    while last_ind<n:
        
        if now>=n:
            return []
        c[queue[now]]=True
        if side_num_arr[queue[now]]<=0:
            now+=1
            continue
        for edge in node[queue[now]]:
            #edge=i[0]
            if side_num_arr[edge]<=0 or c[edge]==True:
                continue
            side_num_arr[edge]-=1
            
            queue[last_ind]=edge
            last_ind+=1
            c[edge]=True
            ans[edge]=queue[now]

        side_num_arr[queue[now]]=0
        now+=1
    return ans



n,m=input_list()
node=[[] for _ in range(n)]

for i in range(m):
    u,v=input_list()
    u-=1
    v-=1
    node[u].append(v)
    node[v].append(u)

#print(np.array(node))

ans=bfs(0,n,node)
if len(ans)==0:
    print("No")
    exit()

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