Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**9)

(N, M), *miti = [[*map(int, line.split())] for line in open(0)]

# print(miti)

A = [list() for _ in range(N+1)]
for m in miti:
    a, b = m
    A[a].append(b)
    A[b].append(a)

# print(A)

ans = [0] * (N + 1)
dist = [N] * (N + 1)


def check(p, d):
    for t in A[p]:
        if d + 1 < dist[t]:
            dist[t] = d + 1
            ans[t] = p
            check(t, d + 1)


dist[1] = 0
ans[1] = 88888
check(1, 0)

dist = dist[1:]
ans = ans[2:]
if all(d < N for d in dist):
    print("Yes")
    for a in ans:
        print(a)
else:
    print("No")

Fixed submission:
(N, M), *miti = [[*map(int, line.split())] for line in open(0)]

# print(miti)

A = [list() for _ in range(N+1)]
for m in miti:
    a, b = m
    A[a].append(b)
    A[b].append(a)

# print(A)

ans = [0] * (N + 1)
dist = [N] * (N + 1)
R = [list() for _ in range(N)]

dist[1] = 0
R[0].append(1)
ans[1] = 88888
for i in range(N):
    for p in R[i]:
        for t in A[p]:
            if i + 1 < dist[t]:
                dist[t] = i + 1
                R[i+1].append(t)
                ans[t] = p

dist = dist[1:]
ans = ans[2:]
if all(d < N for d in dist):
    print("Yes")
    for a in ans:
        print(a)
else:
    print("No")

Buggy python submission (verdict: Runtime Error):
(N, M), *miti = [[*map(int, line.split())] for line in open(0)]

# print(miti)

A = [list() for _ in range(N+1)]
for m in miti:
    a, b = m
    A[a].append(b)
    A[b].append(a)

# print(A)

ans = [0] * (N + 1)
dist = [N] * (N + 1)


def check(p, d):
    for t in A[p]:
        if d + 1 < dist[t]:
            dist[t] = d + 1
            ans[t] = p
            check(t, d + 1)


dist[1] = 0
ans[1] = 88888
check(1, 0)

dist = dist[1:]
ans = ans[2:]
print("foo")
exit()
if all(d < N for d in dist):
    print("Yes")
    for a in ans:
        print(a)
else:
    print("No")

Fixed submission:
(N, M), *miti = [[*map(int, line.split())] for line in open(0)]

# print(miti)

A = [list() for _ in range(N+1)]
for m in miti:
    a, b = m
    A[a].append(b)
    A[b].append(a)

# print(A)

ans = [0] * (N + 1)
dist = [N] * (N + 1)
R = [list() for _ in range(N)]

dist[1] = 0
R[0].append(1)
ans[1] = 88888
for i in range(N):
    for p in R[i]:
        for t in A[p]:
            if i + 1 < dist[t]:
                dist[t] = i + 1
                R[i+1].append(t)
                ans[t] = p

dist = dist[1:]
ans = ans[2:]
if all(d < N for d in dist):
    print("Yes")
    for a in ans:
        print(a)
else:
    print("No")

Buggy python submission (verdict: Runtime Error):
(N, M), *miti = [[*map(int, line.split())] for line in open(0)]

# print(miti)

A = [list() for _ in range(N+1)]
for m in miti:
    a, b = m
    A[a].append(b)
    A[b].append(a)

# print(A)

ans = [0] * (N + 1)
dist = [N] * (N + 1)


def check(p, d):
    for t in A[p]:
        if d + 1 < dist[t]:
            dist[t] = d + 1
            ans[t] = p
            check(t, d + 1)


dist[1] = 0
ans[1] = 88888
check(1, 0)

dist = dist[1:]
ans = ans[2:]
if all(d < N for d in dist):
    print("Yes")
    for a in ans:
        print(a)
else:
    print("No")

Fixed submission:
(N, M), *miti = [[*map(int, line.split())] for line in open(0)]

# print(miti)

A = [list() for _ in range(N+1)]
for m in miti:
    a, b = m
    A[a].append(b)
    A[b].append(a)

# print(A)

ans = [0] * (N + 1)
dist = [N] * (N + 1)
R = [list() for _ in range(N)]

dist[1] = 0
R[0].append(1)
ans[1] = 88888
for i in range(N):
    for p in R[i]:
        for t in A[p]:
            if i + 1 < dist[t]:
                dist[t] = i + 1
                R[i+1].append(t)
                ans[t] = p

dist = dist[1:]
ans = ans[2:]
if all(d < N for d in dist):
    print("Yes")
    for a in ans:
        print(a)
else:
    print("No")