Buggy python submission (verdict: Time Limit Exceeded):
mNM = map(int, input().split())
lNM = list(mNM)

mWay = [map(int, input().split()) for i in range(lNM[1])]
lWay = [list(mWay[i]) for i in range(lNM[1])]

maps = [-1 for i in range(lNM[0])]
deep = [-1 for i in range(lNM[0])]
ways = [[] for i in range(lNM[0])]

for i in range(lNM[1]):
    ways[lWay[i][0] - 1].append(lWay[i][1])
    ways[lWay[i][1] - 1].append(lWay[i][0])

maps[0] = 0
deep[0] = 0

for i in range(lNM[0]):
    try:
        index = [n for n, v in enumerate(deep) if v == i]
        if(index == []):
            break
        
        for x in index:
            for w in ways[x]:
                if(deep[w - 1] == -1):
                    deep[w - 1] = i + 1
                    maps[w - 1] = x + 1
        
    except:
        pass
    
if(-1 in maps):
    print('No')
else:
    print('Yes')
    for i in maps[1:]:
        print(i)

Fixed submission:
mNM = map(int, input().split())
lNM = list(mNM)

mWay = [map(int, input().split()) for i in range(lNM[1])]
lWay = [list(mWay[i]) for i in range(lNM[1])]

maps = [-1 for i in range(lNM[0])]
deep = [-1 for i in range(lNM[0])]
ways = [[] for i in range(lNM[0])]

for i in range(lNM[1]):
    ways[lWay[i][0] - 1].append(lWay[i][1])
    ways[lWay[i][1] - 1].append(lWay[i][0])

maps[0] = 0
deep[0] = 0
nexts = [0]

for i in range(lNM[0]):
    try:
        index = nexts     
        nexts = []
        
        for x in index:
            for w in ways[x]:
                if(deep[w - 1] == -1):
                    deep[w - 1] = i + 1
                    maps[w - 1] = x + 1
                    nexts.append(w - 1)
        
    except:
        pass
    
if(-1 in maps):
    print('No')
else:
    print('Yes')
    for i in maps[1:]:
        print(i)

Buggy python submission (verdict: Time Limit Exceeded):
mNM = map(int, input().split())
lNM = list(mNM)

mWay = [map(int, input().split()) for i in range(lNM[1])]
lWay = [list(mWay[i]) for i in range(lNM[1])]

maps = [-1 for i in range(lNM[0])]
deep = [-1 for i in range(lNM[0])]
ways = [[] for i in range(lNM[0])]

for i in range(lNM[1]):
    ways[lWay[i][0] - 1].append(lWay[i][1])
    ways[lWay[i][1] - 1].append(lWay[i][0])

maps[0] = 0
deep[0] = 0

for i in range(lNM[0]):
    try:
        index = [n for n, v in enumerate(deep) if v == i]
        for x in index:
            for w in ways[x]:
                if(deep[w - 1] == -1):
                    deep[w - 1] = i + 1
                    maps[w - 1] = x + 1
        
    except:
        pass
    
if(-1 in maps):
    print('No')
else:
    print('Yes')
    for i in maps[1:]:
        print(i)

Fixed submission:
mNM = map(int, input().split())
lNM = list(mNM)

mWay = [map(int, input().split()) for i in range(lNM[1])]
lWay = [list(mWay[i]) for i in range(lNM[1])]

maps = [-1 for i in range(lNM[0])]
deep = [-1 for i in range(lNM[0])]
ways = [[] for i in range(lNM[0])]

for i in range(lNM[1]):
    ways[lWay[i][0] - 1].append(lWay[i][1])
    ways[lWay[i][1] - 1].append(lWay[i][0])

maps[0] = 0
deep[0] = 0
nexts = [0]

for i in range(lNM[0]):
    try:
        index = nexts     
        nexts = []
        
        for x in index:
            for w in ways[x]:
                if(deep[w - 1] == -1):
                    deep[w - 1] = i + 1
                    maps[w - 1] = x + 1
                    nexts.append(w - 1)
        
    except:
        pass
    
if(-1 in maps):
    print('No')
else:
    print('Yes')
    for i in maps[1:]:
        print(i)