Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict
from heapq import heappop, heappush


class Graph(object):
    """
    隣接リストによる有向グラフ
    """

    def __init__(self):
        self.graph = defaultdict(list)

    def __len__(self):
        return len(self.graph)

    def add_edge(self, src, dst, weight=1):
        self.graph[src].append((dst, weight))

    def get_nodes(self):
        return self.graph.keys()


class Dijkstra(object):
    """
    ダイクストラ法（二分ヒープ）による最短経路探索
    計算量: O((E+V)logV)
    """

    def __init__(self, graph, start):
        self.g = graph.graph

        # startノードからの最短距離
        # startノードは0, それ以外は無限大で初期化
        self.dist = defaultdict(lambda: float('inf'))
        self.dist[start] = 0

        # 最短経路での1つ前のノード
        self.prev = defaultdict(lambda: None)

        # startノードをキューに入れる
        self.Q = []
        heappush(self.Q, (self.dist[start], start))

        while self.Q:
            # 優先度（距離）が最小であるキューを取り出す
            dist_u, u = heappop(self.Q)
            if self.dist[u] < dist_u:
                continue
            for v, weight in self.g[u]:
                alt = dist_u + weight
                if self.dist[v] > alt:
                    self.dist[v] = alt
                    self.prev[v] = u
                    heappush(self.Q, (alt, v))

    def shortest_distance(self, goal):
        """
        startノードからgoalノードまでの最短距離
        """
        return self.dist[goal]

    def shortest_path(self, goal):
        """
        startノードからgoalノードまでの最短経路
        """
        path = []
        node = goal
        while node is not None:
            path.append(node)
            node = self.prev[node]
        return path[::-1]

n, m = map(int, input().split())
g = Graph()
for i in range(m):
    a, b = map(int, input().split())
    g.add_edge(a-1, b-1, 1)
    g.add_edge(b-1, a-1, 1)

d = Dijkstra(g, 0)
A = []
for i in range(n):
    a = d.shortest_distance(i)
    if a == float('inf'):
        print("No")
        break
    else:
        A.append(d.shortest_distance(i))

if len(A) == n:
    ANS = [0] * n
    for i in range(1, n):
        if ANS[i] == 0:
            B = d.shortest_path(i)
            ANS[B[-1]] = B[-2] + 1
    print("Yes")
    for i in ANS[1:]:
        print(i)

Fixed submission:
from collections import defaultdict
from heapq import heappop, heappush


class Graph(object):
    """
    隣接リストによる有向グラフ
    """

    def __init__(self):
        self.graph = defaultdict(list)

    def __len__(self):
        return len(self.graph)

    def add_edge(self, src, dst, weight=1):
        self.graph[src].append((dst, weight))

    def get_nodes(self):
        return self.graph.keys()


class Dijkstra(object):
    """
    ダイクストラ法（二分ヒープ）による最短経路探索
    計算量: O((E+V)logV)
    """

    def __init__(self, graph, start):
        self.g = graph.graph

        # startノードからの最短距離
        # startノードは0, それ以外は無限大で初期化
        self.dist = defaultdict(lambda: float('inf'))
        self.dist[start] = 0

        # 最短経路での1つ前のノード
        self.prev = defaultdict(lambda: None)

        # startノードをキューに入れる
        self.Q = []
        heappush(self.Q, (self.dist[start], start))

        while self.Q:
            # 優先度（距離）が最小であるキューを取り出す
            dist_u, u = heappop(self.Q)
            if self.dist[u] < dist_u:
                continue
            for v, weight in self.g[u]:
                alt = dist_u + weight
                if self.dist[v] > alt:
                    self.dist[v] = alt
                    self.prev[v] = u
                    heappush(self.Q, (alt, v))

    def shortest_distance(self, goal):
        """
        startノードからgoalノードまでの最短距離
        """
        return self.dist[goal]

    def shortest_path(self, goal):
        """
        startノードからgoalノードまでの最短経路
        """
        path = []
        node = goal
        while node is not None:
            path.append(node)
            node = self.prev[node]
        return path[::-1]
    
    def sp(self, goal):
        path = []
        node = goal
        for _ in range(2):
            path.append(node)
            node = self.prev[node]
        return path[1]

n, m = map(int, input().split())
g = Graph()
for i in range(m):
    a, b = map(int, input().split())
    g.add_edge(a-1, b-1, 1)
    g.add_edge(b-1, a-1, 1)

d = Dijkstra(g, 0)
A = []
# print(d.sp(2))
for i in range(n):
    a = d.shortest_distance(i)
    if a == float('inf'):
        print("No")
        break
    else:
        A.append(d.shortest_distance(i))

if len(A) == n:
    print("Yes")
    for i in range(1, n):
        print(d.sp(i) + 1)

Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict
from heapq import heappop, heappush


class Graph(object):
    """
    隣接リストによる有向グラフ
    """

    def __init__(self):
        self.graph = defaultdict(list)

    def __len__(self):
        return len(self.graph)

    def add_edge(self, src, dst, weight=1):
        self.graph[src].append((dst, weight))

    def get_nodes(self):
        return self.graph.keys()


class Dijkstra(object):
    """
    ダイクストラ法（二分ヒープ）による最短経路探索
    計算量: O((E+V)logV)
    """

    def __init__(self, graph, start):
        self.g = graph.graph

        # startノードからの最短距離
        # startノードは0, それ以外は無限大で初期化
        self.dist = defaultdict(lambda: float('inf'))
        self.dist[start] = 0

        # 最短経路での1つ前のノード
        self.prev = defaultdict(lambda: None)

        # startノードをキューに入れる
        self.Q = []
        heappush(self.Q, (self.dist[start], start))

        while self.Q:
            # 優先度（距離）が最小であるキューを取り出す
            dist_u, u = heappop(self.Q)
            if self.dist[u] < dist_u:
                continue
            for v, weight in self.g[u]:
                alt = dist_u + weight
                if self.dist[v] > alt:
                    self.dist[v] = alt
                    self.prev[v] = u
                    heappush(self.Q, (alt, v))

    def shortest_distance(self, goal):
        """
        startノードからgoalノードまでの最短距離
        """
        return self.dist[goal]

    def shortest_path(self, goal):
        """
        startノードからgoalノードまでの最短経路
        """
        path = []
        node = goal
        while node is not None:
            path.append(node)
            node = self.prev[node]
        return path[::-1]

n, m = map(int, input().split())
g = Graph()
for i in range(m):
    a, b = map(int, input().split())
    g.add_edge(a-1, b-1, 1)
    g.add_edge(b-1, a-1, 1)

d = Dijkstra(g, 0)
A = []
for i in range(n):
    a = d.shortest_distance(i)
    if a == float('inf'):
        print("No")
        break
    else:
        A.append(d.shortest_distance(i))

if len(A) == n:
    ANS = [0] * n
    for i in range(1, n):
        if ANS[i] == 0:
            B = d.shortest_path(i)
            for j in range(A[i]):
                ANS[B[-1-j]] = B[-1-j-1]+1
    # print(ANS)
    print("Yes")
    for i in ANS[1:]:
        print(i)

Fixed submission:
from collections import defaultdict
from heapq import heappop, heappush


class Graph(object):
    """
    隣接リストによる有向グラフ
    """

    def __init__(self):
        self.graph = defaultdict(list)

    def __len__(self):
        return len(self.graph)

    def add_edge(self, src, dst, weight=1):
        self.graph[src].append((dst, weight))

    def get_nodes(self):
        return self.graph.keys()


class Dijkstra(object):
    """
    ダイクストラ法（二分ヒープ）による最短経路探索
    計算量: O((E+V)logV)
    """

    def __init__(self, graph, start):
        self.g = graph.graph

        # startノードからの最短距離
        # startノードは0, それ以外は無限大で初期化
        self.dist = defaultdict(lambda: float('inf'))
        self.dist[start] = 0

        # 最短経路での1つ前のノード
        self.prev = defaultdict(lambda: None)

        # startノードをキューに入れる
        self.Q = []
        heappush(self.Q, (self.dist[start], start))

        while self.Q:
            # 優先度（距離）が最小であるキューを取り出す
            dist_u, u = heappop(self.Q)
            if self.dist[u] < dist_u:
                continue
            for v, weight in self.g[u]:
                alt = dist_u + weight
                if self.dist[v] > alt:
                    self.dist[v] = alt
                    self.prev[v] = u
                    heappush(self.Q, (alt, v))

    def shortest_distance(self, goal):
        """
        startノードからgoalノードまでの最短距離
        """
        return self.dist[goal]

    def shortest_path(self, goal):
        """
        startノードからgoalノードまでの最短経路
        """
        path = []
        node = goal
        while node is not None:
            path.append(node)
            node = self.prev[node]
        return path[::-1]
    
    def sp(self, goal):
        path = []
        node = goal
        for _ in range(2):
            path.append(node)
            node = self.prev[node]
        return path[1]

n, m = map(int, input().split())
g = Graph()
for i in range(m):
    a, b = map(int, input().split())
    g.add_edge(a-1, b-1, 1)
    g.add_edge(b-1, a-1, 1)

d = Dijkstra(g, 0)
A = []
# print(d.sp(2))
for i in range(n):
    a = d.shortest_distance(i)
    if a == float('inf'):
        print("No")
        break
    else:
        A.append(d.shortest_distance(i))

if len(A) == n:
    print("Yes")
    for i in range(1, n):
        print(d.sp(i) + 1)

Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict
from heapq import heappop, heappush


class Graph(object):
    """
    隣接リストによる有向グラフ
    """

    def __init__(self):
        self.graph = defaultdict(list)

    def __len__(self):
        return len(self.graph)

    def add_edge(self, src, dst, weight=1):
        self.graph[src].append((dst, weight))

    def get_nodes(self):
        return self.graph.keys()


class Dijkstra(object):
    """
    ダイクストラ法（二分ヒープ）による最短経路探索
    計算量: O((E+V)logV)
    """

    def __init__(self, graph, start):
        self.g = graph.graph

        # startノードからの最短距離
        # startノードは0, それ以外は無限大で初期化
        self.dist = defaultdict(lambda: float('inf'))
        self.dist[start] = 0

        # 最短経路での1つ前のノード
        self.prev = defaultdict(lambda: None)

        # startノードをキューに入れる
        self.Q = []
        heappush(self.Q, (self.dist[start], start))

        while self.Q:
            # 優先度（距離）が最小であるキューを取り出す
            dist_u, u = heappop(self.Q)
            if self.dist[u] < dist_u:
                continue
            for v, weight in self.g[u]:
                alt = dist_u + weight
                if self.dist[v] > alt:
                    self.dist[v] = alt
                    self.prev[v] = u
                    heappush(self.Q, (alt, v))

    def shortest_distance(self, goal):
        """
        startノードからgoalノードまでの最短距離
        """
        return self.dist[goal]

    def shortest_path(self, goal):
        """
        startノードからgoalノードまでの最短経路
        """
        path = []
        node = goal
        while node is not None:
            path.append(node)
            node = self.prev[node]
        return path[::-1]

n, m = map(int, input().split())
g = Graph()
for i in range(m):
    a, b = map(int, input().split())
    g.add_edge(a-1, b-1, 1)
    g.add_edge(b-1, a-1, 1)

d = Dijkstra(g, 0)
A = []
for i in range(n):
    A.append(d.shortest_distance(i))


if float('inf') in A:
    print("No")
else:
    print("Yes")
    for i in range(1, n):
        print(d.shortest_path(i)[-2] + 1)

Fixed submission:
from collections import defaultdict
from heapq import heappop, heappush


class Graph(object):
    """
    隣接リストによる有向グラフ
    """

    def __init__(self):
        self.graph = defaultdict(list)

    def __len__(self):
        return len(self.graph)

    def add_edge(self, src, dst, weight=1):
        self.graph[src].append((dst, weight))

    def get_nodes(self):
        return self.graph.keys()


class Dijkstra(object):
    """
    ダイクストラ法（二分ヒープ）による最短経路探索
    計算量: O((E+V)logV)
    """

    def __init__(self, graph, start):
        self.g = graph.graph

        # startノードからの最短距離
        # startノードは0, それ以外は無限大で初期化
        self.dist = defaultdict(lambda: float('inf'))
        self.dist[start] = 0

        # 最短経路での1つ前のノード
        self.prev = defaultdict(lambda: None)

        # startノードをキューに入れる
        self.Q = []
        heappush(self.Q, (self.dist[start], start))

        while self.Q:
            # 優先度（距離）が最小であるキューを取り出す
            dist_u, u = heappop(self.Q)
            if self.dist[u] < dist_u:
                continue
            for v, weight in self.g[u]:
                alt = dist_u + weight
                if self.dist[v] > alt:
                    self.dist[v] = alt
                    self.prev[v] = u
                    heappush(self.Q, (alt, v))

    def shortest_distance(self, goal):
        """
        startノードからgoalノードまでの最短距離
        """
        return self.dist[goal]

    def shortest_path(self, goal):
        """
        startノードからgoalノードまでの最短経路
        """
        path = []
        node = goal
        while node is not None:
            path.append(node)
            node = self.prev[node]
        return path[::-1]
    
    def sp(self, goal):
        path = []
        node = goal
        for _ in range(2):
            path.append(node)
            node = self.prev[node]
        return path[1]

n, m = map(int, input().split())
g = Graph()
for i in range(m):
    a, b = map(int, input().split())
    g.add_edge(a-1, b-1, 1)
    g.add_edge(b-1, a-1, 1)

d = Dijkstra(g, 0)
A = []
# print(d.sp(2))
for i in range(n):
    a = d.shortest_distance(i)
    if a == float('inf'):
        print("No")
        break
    else:
        A.append(d.shortest_distance(i))

if len(A) == n:
    print("Yes")
    for i in range(1, n):
        print(d.sp(i) + 1)