Buggy python submission (verdict: Time Limit Exceeded):
# https://qiita.com/kazukazukazukazu/items/e5db00a3aefb1f5ed72f
import collections
import heapq


class Dijkstra():
    def __init__(self):
        self.e = collections.defaultdict(list)

    def add(self, u, v, d, directed=False):
        """
        #0-indexedでなくてもよいことに注意
        #u = from, v = to, d = cost
        #directed = Trueなら、有向グラフである
        """
        if directed is False:
            self.e[u].append([v, d])
            self.e[v].append([u, d])
        else:
            self.e[u].append([v, d])

    def delete(self, u, v):
        self.e[u] = [_ for _ in self.e[u] if _[0] != v]
        self.e[v] = [_ for _ in self.e[v] if _[0] != u]

    def Dijkstra_search(self, s):
        """
        #0-indexedでなくてもよいことに注意
        #:param s: 始点
        #:return: 始点から各点までの最短経路と最短経路を求めるのに必要なprev
        """
        d = collections.defaultdict(lambda: float('inf'))
        prev = collections.defaultdict(lambda: None)
        d[s] = 0
        q = []
        heapq.heappush(q, (0, s))
        v = collections.defaultdict(bool)
        while len(q):
            k, u = heapq.heappop(q)
            if v[u]:
                continue
            v[u] = True

            for uv, ud in self.e[u]:
                if v[uv]:
                    continue
                vd = k + ud
                if d[uv] > vd:
                    d[uv] = vd
                    prev[uv] = u
                    heapq.heappush(q, (vd, uv))

        return d, prev

    def getDijkstraShortestPath(self, start, goal):
        _, prev = self.Dijkstra_search(start)
        shortestPath = []
        node = goal
        while node is not None:
            shortestPath.append(node)
            node = prev[node]
        return shortestPath[::-1]

N, M = map(int, input().split())
# AB = [[int(x) for x in input().split()] for _ in range(M)]

graph = Dijkstra()

for _ in range(M):
    a, b = map(int, input().split())
    graph.add(a, b, 1)

# for a, b in AB:
#     graph.add(a, b, 1)

ans = [float('inf')] * (N-1)
flg = False
for i in range(2, N+1):
    result = graph.getDijkstraShortestPath(i, 1)
    if result[1]==float('inf'):
        flg = True
        break
    ans[i-2] = result[1]
#     print(result[1])

if flg:
    print('No')
else:
    print('Yes')
    for a in ans:
        print(a)
    
    

Fixed submission:
import collections
N, M = map(int, input().split())
G = collections.defaultdict(list)
for _ in range(M):
    a, b = map(int, input().split())
    G[a].append(b)
    G[b].append(a)
    
dist = [-1] * (N + 1)
que = collections.deque()

dist[1] = 0
que.append(1)

while len(que):
    v = que.popleft()
    for nv in G[v]:
        if dist[nv] != -1:
            continue
        dist[nv] = dist[v] + 1
        que.append(nv)

memo = collections.defaultdict(int)
memo[0] = 1

print('Yes')
for i in range(2, N+1):
    memo[dist[i]] = i
for dis in dist[2:]:
    print(memo[dis-1])

Buggy python submission (verdict: Time Limit Exceeded):
# https://qiita.com/kazukazukazukazu/items/e5db00a3aefb1f5ed72f
import collections
import heapq


class Dijkstra():
    def __init__(self):
        self.e = collections.defaultdict(list)

    def add(self, u, v, d, directed=False):
        """
        #0-indexedでなくてもよいことに注意
        #u = from, v = to, d = cost
        #directed = Trueなら、有向グラフである
        """
        if directed is False:
            self.e[u].append([v, d])
            self.e[v].append([u, d])
        else:
            self.e[u].append([v, d])

    def delete(self, u, v):
        self.e[u] = [_ for _ in self.e[u] if _[0] != v]
        self.e[v] = [_ for _ in self.e[v] if _[0] != u]

    def Dijkstra_search(self, s):
        """
        #0-indexedでなくてもよいことに注意
        #:param s: 始点
        #:return: 始点から各点までの最短経路と最短経路を求めるのに必要なprev
        """
        d = collections.defaultdict(lambda: float('inf'))
        prev = collections.defaultdict(lambda: None)
        d[s] = 0
        q = []
        heapq.heappush(q, (0, s))
        v = collections.defaultdict(bool)
        while len(q):
            k, u = heapq.heappop(q)
            if v[u]:
                continue
            v[u] = True

            for uv, ud in self.e[u]:
                if v[uv]:
                    continue
                vd = k + ud
                if d[uv] > vd:
                    d[uv] = vd
                    prev[uv] = u
                    heapq.heappush(q, (vd, uv))

        return d, prev

    def getDijkstraShortestPath(self, start, goal):
        _, prev = self.Dijkstra_search(start)
        shortestPath = []
        node = goal
        while node is not None:
            shortestPath.append(node)
            node = prev[node]
        return shortestPath[::-1]

N, M = map(int, input().split())
# AB = [[int(x) for x in input().split()] for _ in range(M)]

graph = Dijkstra()

for _ in range(M):
    a, b = map(int, input().split())
    graph.add(a, b, 1)

# for a, b in AB:
#     graph.add(a, b, 1)

ans = []
flg = False
for i in range(2, N+1):
    result = graph.getDijkstraShortestPath(i, 1)
    if result[1]==float('inf'):
        flg = True
        break
    ans.append(result[1])
#     print(result[1])

if flg:
    print('No')
else:
    print('Yes')
    for a in ans:
        print(a)
    
    

Fixed submission:
import collections
N, M = map(int, input().split())
G = collections.defaultdict(list)
for _ in range(M):
    a, b = map(int, input().split())
    G[a].append(b)
    G[b].append(a)
    
dist = [-1] * (N + 1)
que = collections.deque()

dist[1] = 0
que.append(1)

while len(que):
    v = que.popleft()
    for nv in G[v]:
        if dist[nv] != -1:
            continue
        dist[nv] = dist[v] + 1
        que.append(nv)

memo = collections.defaultdict(int)
memo[0] = 1

print('Yes')
for i in range(2, N+1):
    memo[dist[i]] = i
for dis in dist[2:]:
    print(memo[dis-1])

Buggy python submission (verdict: Time Limit Exceeded):
# https://qiita.com/kazukazukazukazu/items/e5db00a3aefb1f5ed72f
import collections
import heapq


class Dijkstra():
    def __init__(self):
        self.e = collections.defaultdict(list)

    def add(self, u, v, d, directed=False):
        """
        #0-indexedでなくてもよいことに注意
        #u = from, v = to, d = cost
        #directed = Trueなら、有向グラフである
        """
        if directed is False:
            self.e[u].append([v, d])
            self.e[v].append([u, d])
        else:
            self.e[u].append([v, d])

    def delete(self, u, v):
        self.e[u] = [_ for _ in self.e[u] if _[0] != v]
        self.e[v] = [_ for _ in self.e[v] if _[0] != u]

    def Dijkstra_search(self, s):
        """
        #0-indexedでなくてもよいことに注意
        #:param s: 始点
        #:return: 始点から各点までの最短経路と最短経路を求めるのに必要なprev
        """
        d = collections.defaultdict(lambda: float('inf'))
        prev = collections.defaultdict(lambda: None)
        d[s] = 0
        q = []
        heapq.heappush(q, (0, s))
        v = collections.defaultdict(bool)
        while len(q):
            k, u = heapq.heappop(q)
            if v[u]:
                continue
            v[u] = True

            for uv, ud in self.e[u]:
                if v[uv]:
                    continue
                vd = k + ud
                if d[uv] > vd:
                    d[uv] = vd
                    prev[uv] = u
                    heapq.heappush(q, (vd, uv))

        return d, prev

    def getDijkstraShortestPath(self, start, goal):
        _, prev = self.Dijkstra_search(start)
        shortestPath = []
        node = goal
        while node is not None:
            shortestPath.append(node)
            node = prev[node]
        return shortestPath[::-1]

N, M = map(int, input().split())
AB = [[int(x) for x in input().split()] for _ in range(M)]

graph = Dijkstra()

for a, b in AB:
    graph.add(a, b, 1)

ans = []
for i in range(2, N+1):
    result = graph.getDijkstraShortestPath(i, 1)
    ans.append(result[1])
#     print(result[1])

if float('inf') in ans:
    print('No')
else:
    print('Yes')
    for a in ans:
        print(a)
    
    

Fixed submission:
import collections
N, M = map(int, input().split())
G = collections.defaultdict(list)
for _ in range(M):
    a, b = map(int, input().split())
    G[a].append(b)
    G[b].append(a)
    
dist = [-1] * (N + 1)
que = collections.deque()

dist[1] = 0
que.append(1)

while len(que):
    v = que.popleft()
    for nv in G[v]:
        if dist[nv] != -1:
            continue
        dist[nv] = dist[v] + 1
        que.append(nv)

memo = collections.defaultdict(int)
memo[0] = 1

print('Yes')
for i in range(2, N+1):
    memo[dist[i]] = i
for dis in dist[2:]:
    print(memo[dis-1])