Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10 ** 5 + 10)
def input(): return sys.stdin.readline().strip()

def resolve():
    
    # https://atcoder.jp/contests/abc070/tasks/abc070_d
    # https://atcoder.jp/contests/abc070/submissions/11681543
    from heapq import heapify, heappop, heappush
    
    N ,M= map(int,input().split())
    inf = 10 ** 17
    
    
    def dijkstra_heap(start, edge):
        # 始点から各頂点への最短距離(頂点番号:0~N-1)
        d = [inf] * N
        used = [False] * N
        d[start] = 0
        used[start] = True
        edgelist = []
        # a:重み(//), b:次の頂点(%)
        for a, b in edge[start]:
            heappush(edgelist, a * (10 ** 6) + b)
    
        while len(edgelist):
            # まだ最短距離が決まっていない頂点の中から最小の距離のものを探す
            minedge = heappop(edgelist)
            if used[minedge % (10 ** 6)]:
                continue
            node = minedge % (10 ** 6)
            d[node] = minedge // (10 ** 6)
            used[node] = True
    
            for e in edge[node]:
                if not used[e[1]]:
                    heappush(edgelist, (e[0] + d[node]) * (10 ** 6) + e[1])
        return d
    
    
    # N:頂点数   W:辺数
    edge = [[] for i in range(N)]
    # edge[i] : iから出る道の[重み,行先]の配列
    for _ in range(M):
        a, b= map(int, input().split())
        edge[a - 1].append((1, b - 1))
        edge[b - 1].append((1, a - 1))
    
    d = dijkstra_heap(0, edge)
    
    def main():
        mark=[0]+[-1]*(N-1)
        times=[0]+[-1]*(N-1)
        cur=1
        for i in range(1,N):
            if d[i]==1:
                mark[i]=0
                times[i]=cur
        cur+=1
        cnt=False
        while True:
            if -1 not in mark:
                break
            for i in range(1,N):
                if d[i]==cur:
                    cnt=True
                    for k in range(len(edge[i])):
                        if times[edge[i][k][1]]==cur-1:
                            mark[i]=edge[i][k][1]
                            times[i]=cur
                            cnt+=1
                            break
                        else:
                            if k==len(edge[i])-1:
                                return False
            if not cnt:
                return False
            else:
                cur+=1
                cnt=False
        
        return mark[1:]
    
    if main():
        print('Yes')
        for i in main():
            print(i+1)
    else: print('No')
        



    
resolve()

Fixed submission:
import sys
sys.setrecursionlimit(10 ** 5 + 10)


def input(): return sys.stdin.readline().strip()


def resolve():

    # https://atcoder.jp/contests/abc070/tasks/abc070_d
    # https://atcoder.jp/contests/abc070/submissions/11681543
    from heapq import heapify, heappop, heappush

    N, M = map(int, input().split())
    inf = 10 ** 17

    def dijkstra_heap(start, edge):
        # 始点から各頂点への最短距離(頂点番号:0~N-1)
        d = [inf] * N
        used = [False] * N
        d[start] = 0
        used[start] = True
        edgelist = []
        # a:重み(//), b:次の頂点(%)
        for a, b in edge[start]:
            heappush(edgelist, a * (10 ** 6) + b)

        while len(edgelist):
            # まだ最短距離が決まっていない頂点の中から最小の距離のものを探す
            minedge = heappop(edgelist)
            if used[minedge % (10 ** 6)]:
                continue
            node = minedge % (10 ** 6)
            d[node] = minedge // (10 ** 6)
            used[node] = True

            for e in edge[node]:
                if not used[e[1]]:
                    heappush(edgelist, (e[0] + d[node]) * (10 ** 6) + e[1])
        return d

    # N:頂点数   W:辺数
    edge = [[] for i in range(N)]
    # edge[i] : iから出る道の[重み,行先]の配列
    for _ in range(M):
        a, b = map(int, input().split())
        edge[a - 1].append((1, b - 1))
        edge[b - 1].append((1, a - 1))

    d = dijkstra_heap(0, edge)
    max_times = max(d)

    times_list = [[] for _ in range(max_times+1)]
    for id, val in enumerate(d):
        times_list[val].append(id)

    def main():
        mark = [0]+[-1]*(N-1)
        cur = 1
        for i in range(1, N):
            if d[i] == 1:
                mark[i] = 0
            else:
                if times_list[d[i]-1]:
                    mark[i]=times_list[d[i]-1][0]
                else:
                    return False
        return mark[1:]

    if main():
        print('Yes')
        for i in main():
            print(i+1)
    else:
        print('No')

resolve()