Buggy python submission (verdict: Time Limit Exceeded):
from sys import stdin
import sys

sys.setrecursionlimit(10**5)

class DFS():
    def __init__(self,A_B_arr,N,M):
        self.N = N
        self.M = M
        self.route = {i:[] for i in range(N+1)}
        for A, B in A_B_arr:
            self.route[A].append(B)
            self.route[B].append(A)

        self.dp = [[None,N] for i in range(N+1)]
        self.dp[1] = [1,0]

    def dfs(self,i,rank):
        for r in self.route[i]:
            if rank<self.dp[r][1] and rank<self.N:
                self.dp[r] = [i,rank]
                self.dfs(r,rank+1)
        return


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    dfs = DFS(A_B_arr,N,M)
    dfs.dfs(1,1)

    ans = []
    TF = 'Yes'
    for (i,_) in enumerate(dfs.dp):
        if i>1:
            if _[0] == None:
                TF = 'No'
                break
            else:
                ans.append(_[0])
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if TF == 'Yes':
        print(TF)
        for _ in ans:
            print(_)
    else:
        print(TF)


Fixed submission:
from sys import stdin
from collections import deque


class BFS():
    def __init__(self, con, val=None):
        # 隣接リスト表現
        self.con = con
        self.val = val
        self.N = len(self.con)
        # 1つ前の部屋(1-indexed)
        self.dist = [-1]*self.N
        self.que = deque()

        # 初期条件(0-indexed)
        self.dist[0] = 0
        self.que.append(0)

    def bfs(self):
        while self.que:
            v = self.que.popleft()
            for next_v in self.con[v]:
                if self.dist[next_v] != -1:
                    continue
                self.dist[next_v] = v+1
                self.que.append(next_v)


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    con = [[] for i in range(N)]
    for A,B in A_B_arr:
        A -= 1
        B -= 1
        con[A].append(B)
        con[B].append(A)

    bfs = BFS(con)
    bfs.bfs()
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if -1 in bfs.dist[1:]:
        print('No')
    else:
        print('Yes')
        for _ in bfs.dist[1:]:
            print(_)

Buggy python submission (verdict: Runtime Error):
from sys import stdin


class DFS():
    def __init__(self,A_B_arr,N,M):
        self.N = N
        self.M = M
        self.route = {i:[] for i in range(N+1)}
        for A, B in A_B_arr:
            self.route[A].append(B)
            self.route[B].append(A)

        self.dp = [[None,N] for i in range(N+1)]
        self.dp[1] = [1,0]

    def dfs(self,i,rank):
        for r in self.route[i]:
            if rank<self.dp[r][1] and rank<self.N:
                self.dp[r] = [i,rank]
                self.dfs(r,rank+1)
        return


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    dfs = DFS(A_B_arr,N,M)
    dfs.dfs(1,1)

    ans = []
    TF = 'Yes'
    for (i,_) in enumerate(dfs.dp):
        if i>1:
            if _[0] == None:
                TF = 'No'
                break
            else:
                ans.append(_[0])
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if TF == 'Yes':
        print(TF)
        for _ in ans:
            print(_)
    else:
        print(TF)


Fixed submission:
from sys import stdin
from collections import deque


class BFS():
    def __init__(self, con, val=None):
        # 隣接リスト表現
        self.con = con
        self.val = val
        self.N = len(self.con)
        # 1つ前の部屋(1-indexed)
        self.dist = [-1]*self.N
        self.que = deque()

        # 初期条件(0-indexed)
        self.dist[0] = 0
        self.que.append(0)

    def bfs(self):
        while self.que:
            v = self.que.popleft()
            for next_v in self.con[v]:
                if self.dist[next_v] != -1:
                    continue
                self.dist[next_v] = v+1
                self.que.append(next_v)


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    con = [[] for i in range(N)]
    for A,B in A_B_arr:
        A -= 1
        B -= 1
        con[A].append(B)
        con[B].append(A)

    bfs = BFS(con)
    bfs.bfs()
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if -1 in bfs.dist[1:]:
        print('No')
    else:
        print('Yes')
        for _ in bfs.dist[1:]:
            print(_)

Buggy python submission (verdict: Runtime Error):
from sys import stdin


class DFS():
    def __init__(self,A_B_arr,N,M):
        self.N = N
        self.M = M
        self.route = {i:[] for i in range(N+1)}
        for A, B in A_B_arr:
            self.route[A].append(B)
            self.route[B].append(A)

        self.dp = [[None,N] for i in range(N+1)]
        self.dp[1] = [1,0]
        self.finished = [False for i in range(N+1)]

    def dfs(self,i,rank):
        for r in self.route[i]:
            if rank<self.dp[r][1]:
                self.dp[r] = [i,rank]
                self.dfs(r,rank+1)
        self.route[i] = []
        return


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    dfs = DFS(A_B_arr,N,M)
    dfs.dfs(1,1)

    ans = []
    TF = 'Yes'
    for (i,_) in enumerate(dfs.dp):
        if i>1:
            if _[0] == None:
                TF = 'No'
                break
            else:
                ans.append(_[0])
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if TF == 'Yes':
        print(TF)
        for _ in ans:
            print(_)
    else:
        print(TF)


Fixed submission:
from sys import stdin
from collections import deque


class BFS():
    def __init__(self, con, val=None):
        # 隣接リスト表現
        self.con = con
        self.val = val
        self.N = len(self.con)
        # 1つ前の部屋(1-indexed)
        self.dist = [-1]*self.N
        self.que = deque()

        # 初期条件(0-indexed)
        self.dist[0] = 0
        self.que.append(0)

    def bfs(self):
        while self.que:
            v = self.que.popleft()
            for next_v in self.con[v]:
                if self.dist[next_v] != -1:
                    continue
                self.dist[next_v] = v+1
                self.que.append(next_v)


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    con = [[] for i in range(N)]
    for A,B in A_B_arr:
        A -= 1
        B -= 1
        con[A].append(B)
        con[B].append(A)

    bfs = BFS(con)
    bfs.bfs()
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if -1 in bfs.dist[1:]:
        print('No')
    else:
        print('Yes')
        for _ in bfs.dist[1:]:
            print(_)

Buggy python submission (verdict: Runtime Error):
from sys import stdin


class DFS():
    def __init__(self,A_B_arr,N,M):
        self.N = N
        self.M = M
        self.route = {i:[] for i in range(N+1)}
        for A, B in A_B_arr:
            self.route[A].append(B)
            self.route[B].append(A)

        self.dp = [[None,self.N] for i in range(N+1)]
        self.dp[1] = [1,0]

    def dfs(self,i,rank):
        for r in self.route[i]:
            if rank<self.dp[r][1]:
                self.dp[r] = [i,rank]
                self.dfs(r,rank+1)
        return


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    dfs = DFS(A_B_arr,N,M)
    dfs.dfs(1,1)

    #ans = []
    #TF = 'Yes'
    #for (i,_) in enumerate(dfs.dp):
    #    if i>1:
    #        if _[0] == None:
    #            TF = 'No'
    #            break
    #        else:
    #            ans.append(_[0])
    ## ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    #if TF == 'Yes':
    #    print(TF)
    #    for _ in ans:
    #        print(_)
    #else:
    #    print(TF)


Fixed submission:
from sys import stdin
from collections import deque


class BFS():
    def __init__(self, con, val=None):
        # 隣接リスト表現
        self.con = con
        self.val = val
        self.N = len(self.con)
        # 1つ前の部屋(1-indexed)
        self.dist = [-1]*self.N
        self.que = deque()

        # 初期条件(0-indexed)
        self.dist[0] = 0
        self.que.append(0)

    def bfs(self):
        while self.que:
            v = self.que.popleft()
            for next_v in self.con[v]:
                if self.dist[next_v] != -1:
                    continue
                self.dist[next_v] = v+1
                self.que.append(next_v)


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    con = [[] for i in range(N)]
    for A,B in A_B_arr:
        A -= 1
        B -= 1
        con[A].append(B)
        con[B].append(A)

    bfs = BFS(con)
    bfs.bfs()
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if -1 in bfs.dist[1:]:
        print('No')
    else:
        print('Yes')
        for _ in bfs.dist[1:]:
            print(_)

Buggy python submission (verdict: Runtime Error):
from sys import stdin


class DFS():
    def __init__(self,A_B_arr,N,M):
        self.N = N
        self.M = M
        self.route = {i:[] for i in range(N+1)}
        for A, B in A_B_arr:
            self.route[A].append(B)
            self.route[B].append(A)

        self.dp = [[None,self.N] for i in range(N+1)]
        self.dp[1] = [1,0]

    def dfs(self,i,rank):
        for r in self.route[i]:
            if rank<self.dp[r][1]:
                self.dp[r] = [i,rank]
                self.dfs(r,rank+1)
        return


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    dfs = DFS(A_B_arr,N,M)
    dfs.dfs(1,1)

    ans = []
    TF = 'Yes'
    for (i,_) in enumerate(dfs.dp):
        if i>1:
            if _[0] == None:
                TF = 'No'
                break
            else:
                ans.append(_[0])
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if TF == 'Yes':
        print(TF)
        for _ in ans:
            print(_)
    else:
        print(TF)


Fixed submission:
from sys import stdin
from collections import deque


class BFS():
    def __init__(self, con, val=None):
        # 隣接リスト表現
        self.con = con
        self.val = val
        self.N = len(self.con)
        # 1つ前の部屋(1-indexed)
        self.dist = [-1]*self.N
        self.que = deque()

        # 初期条件(0-indexed)
        self.dist[0] = 0
        self.que.append(0)

    def bfs(self):
        while self.que:
            v = self.que.popleft()
            for next_v in self.con[v]:
                if self.dist[next_v] != -1:
                    continue
                self.dist[next_v] = v+1
                self.que.append(next_v)


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    con = [[] for i in range(N)]
    for A,B in A_B_arr:
        A -= 1
        B -= 1
        con[A].append(B)
        con[B].append(A)

    bfs = BFS(con)
    bfs.bfs()
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if -1 in bfs.dist[1:]:
        print('No')
    else:
        print('Yes')
        for _ in bfs.dist[1:]:
            print(_)

Buggy python submission (verdict: Runtime Error):
from sys import stdin


class DFS():
    def __init__(self,A_B_arr,N,M):
        self.N = N
        self.M = M
        self.route = {i:[] for i in range(N+1)}
        for A, B in A_B_arr:
            self.route[A].append(B)
            self.route[B].append(A)

        self.dp = [[None,float('inf')] for i in range(N+1)]
        self.dp[1] = [1,0]

    def dfs(self,i,rank):
        if rank>self.N:
            return
        else:
            for r in self.route[i]:
                if rank<self.dp[r][1]:
                    self.dp[r] = [i,rank]
                    self.dfs(r,rank+1)
            return


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    dfs = DFS(A_B_arr,N,M)
    dfs.dfs(1,1)

    ans = []
    for (i,_) in enumerate(dfs.dp):
        if i>1 and _[0] == None:
            TF = 'No'
            break
        else:
            ans.append(_[0])
    else:
        TF = 'Yes'
        ans = ans[2:]
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if TF == 'Yes':
        print(TF)
        for _ in ans:
            print(_)
    else:
        print(TF)


Fixed submission:
from sys import stdin
from collections import deque


class BFS():
    def __init__(self, con, val=None):
        # 隣接リスト表現
        self.con = con
        self.val = val
        self.N = len(self.con)
        # 1つ前の部屋(1-indexed)
        self.dist = [-1]*self.N
        self.que = deque()

        # 初期条件(0-indexed)
        self.dist[0] = 0
        self.que.append(0)

    def bfs(self):
        while self.que:
            v = self.que.popleft()
            for next_v in self.con[v]:
                if self.dist[next_v] != -1:
                    continue
                self.dist[next_v] = v+1
                self.que.append(next_v)


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    con = [[] for i in range(N)]
    for A,B in A_B_arr:
        A -= 1
        B -= 1
        con[A].append(B)
        con[B].append(A)

    bfs = BFS(con)
    bfs.bfs()
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if -1 in bfs.dist[1:]:
        print('No')
    else:
        print('Yes')
        for _ in bfs.dist[1:]:
            print(_)

Buggy python submission (verdict: Runtime Error):
from sys import stdin


class DFS():
    def __init__(self,A_B_arr,N,M):
        self.N = N
        self.M = M
        self.route = {i:[] for i in range(N+1)}
        for A, B in A_B_arr:
            self.route[A].append(B)
            self.route[B].append(A)

        self.dp = [[None,float('inf')] for i in range(N+1)]

    def dfs(self,i,rank):
        for r in self.route[i]:
            if rank<self.dp[r][1]:
                self.dp[r] = [i,rank]
                self.dfs(r,rank+1)
        return


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    dfs = DFS(A_B_arr,N,M)
    dfs.dfs(1,1)

    ans = []
    for (i,_) in enumerate(dfs.dp):
        if i>1 and _[0] == None:
            TF = 'No'
            break
        else:
            ans.append(_[0])
    else:
        TF = 'Yes'
        ans = ans[2:]
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if TF == 'Yes':
        print(TF)
        for _ in ans:
            print(_)
    else:
        print(TF)


Fixed submission:
from sys import stdin
from collections import deque


class BFS():
    def __init__(self, con, val=None):
        # 隣接リスト表現
        self.con = con
        self.val = val
        self.N = len(self.con)
        # 1つ前の部屋(1-indexed)
        self.dist = [-1]*self.N
        self.que = deque()

        # 初期条件(0-indexed)
        self.dist[0] = 0
        self.que.append(0)

    def bfs(self):
        while self.que:
            v = self.que.popleft()
            for next_v in self.con[v]:
                if self.dist[next_v] != -1:
                    continue
                self.dist[next_v] = v+1
                self.que.append(next_v)


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    con = [[] for i in range(N)]
    for A,B in A_B_arr:
        A -= 1
        B -= 1
        con[A].append(B)
        con[B].append(A)

    bfs = BFS(con)
    bfs.bfs()
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if -1 in bfs.dist[1:]:
        print('No')
    else:
        print('Yes')
        for _ in bfs.dist[1:]:
            print(_)

Buggy python submission (verdict: Runtime Error):
from sys import stdin


class DFS():
    def __init__(self,A_B_arr,N,M):
        self.N = N
        self.M = M
        self.route = {i:[] for i in range(N+1)}
        for A, B in A_B_arr:
            self.route[A].append(B)
            self.route[B].append(A)

        self.dp = [[None,float('inf')] for i in range(N+1)]

    def dfs(self,i,rank):
        for r in self.route[i]:
            if rank<self.dp[r][1]:
                self.dp[r] = [i,rank]
                self.dfs(r,rank+1)
        return


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    dfs = DFS(A_B_arr,N,M)
    dfs.dfs(1,1)


    print(dfs.dp)
    ans = []
    for (i,_) in enumerate(dfs.dp):
        if i>1 and _[0] == None:
            TF = 'No'
            break
        else:
            ans.append(_[0])
    else:
        TF = 'Yes'
        ans = ans[2:]
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if TF == 'Yes':
        print(TF)
        for _ in ans:
            print(_)
    else:
        print(TF)


Fixed submission:
from sys import stdin
from collections import deque


class BFS():
    def __init__(self, con, val=None):
        # 隣接リスト表現
        self.con = con
        self.val = val
        self.N = len(self.con)
        # 1つ前の部屋(1-indexed)
        self.dist = [-1]*self.N
        self.que = deque()

        # 初期条件(0-indexed)
        self.dist[0] = 0
        self.que.append(0)

    def bfs(self):
        while self.que:
            v = self.que.popleft()
            for next_v in self.con[v]:
                if self.dist[next_v] != -1:
                    continue
                self.dist[next_v] = v+1
                self.que.append(next_v)


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    N, M = list(map(int,_in[0].split(' ')))  # type:list(int)
    A_B_arr = []
    for i in range(M):
        _ = list(map(int,_in[i+1].split(' ')))  # type:list(int)
        A_B_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    con = [[] for i in range(N)]
    for A,B in A_B_arr:
        A -= 1
        B -= 1
        con[A].append(B)
        con[B].append(A)

    bfs = BFS(con)
    bfs.bfs()
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    if -1 in bfs.dist[1:]:
        print('No')
    else:
        print('Yes')
        for _ in bfs.dist[1:]:
            print(_)