Buggy python submission (verdict: Time Limit Exceeded):
import sys, os, math, bisect, itertools, collections, heapq, queue, copy, array

# from scipy.sparse.csgraph import csgraph_from_dense, floyd_warshall
# from decimal import Decimal
# from collections import defaultdict, deque

sys.setrecursionlimit(10000000)

ii = lambda: int(sys.stdin.buffer.readline().rstrip())
il = lambda: list(map(int, sys.stdin.buffer.readline().split()))
fl = lambda: list(map(float, sys.stdin.buffer.readline().split()))
iln = lambda n: [int(sys.stdin.buffer.readline().rstrip()) for _ in range(n)]

iss = lambda: sys.stdin.buffer.readline().decode().rstrip()
sl = lambda: list(map(str, sys.stdin.buffer.readline().decode().split()))
isn = lambda n: [sys.stdin.buffer.readline().decode().rstrip() for _ in range(n)]

lcm = lambda x, y: (x * y) // math.gcd(x, y)

MOD = 10 ** 9 + 7
INF = float('inf')


def main():
    if os.getenv("LOCAL"):
        sys.stdin = open("input.txt", "r")

    N, M = il()
    ret = 0
    while M >= 2:
        if N >= 1 and M >= 2:
            ret += 1
            M -= 2
            N -= 1
        if N == 0 and M >= 2:
            N += 1
            M -= 2
    print(ret)


if __name__ == '__main__':
    main()


Fixed submission:
import sys, os, math, bisect, itertools, collections, heapq, queue, copy, array

# from scipy.sparse.csgraph import csgraph_from_dense, floyd_warshall
# from decimal import Decimal
# from collections import defaultdict, deque

sys.setrecursionlimit(10000000)

ii = lambda: int(sys.stdin.buffer.readline().rstrip())
il = lambda: list(map(int, sys.stdin.buffer.readline().split()))
fl = lambda: list(map(float, sys.stdin.buffer.readline().split()))
iln = lambda n: [int(sys.stdin.buffer.readline().rstrip()) for _ in range(n)]

iss = lambda: sys.stdin.buffer.readline().decode().rstrip()
sl = lambda: list(map(str, sys.stdin.buffer.readline().decode().split()))
isn = lambda n: [sys.stdin.buffer.readline().decode().rstrip() for _ in range(n)]

lcm = lambda x, y: (x * y) // math.gcd(x, y)

MOD = 10 ** 9 + 7
INF = float('inf')


def main():
    if os.getenv("LOCAL"):
        sys.stdin = open("input.txt", "r")

    N, M = il()

    ret = 0
    if N * 2 <= M:
        ret += N
        ret += (M - N * 2) // 4
    else:
        ret += M // 2
    print(ret)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys, os, math, bisect, itertools, collections, heapq, queue, copy, array

# from scipy.sparse.csgraph import csgraph_from_dense, floyd_warshall
# from decimal import Decimal
# from collections import defaultdict, deque

sys.setrecursionlimit(10000000)

ii = lambda: int(sys.stdin.buffer.readline().rstrip())
il = lambda: list(map(int, sys.stdin.buffer.readline().split()))
fl = lambda: list(map(float, sys.stdin.buffer.readline().split()))
iln = lambda n: [int(sys.stdin.buffer.readline().rstrip()) for _ in range(n)]

iss = lambda: sys.stdin.buffer.readline().decode().rstrip()
sl = lambda: list(map(str, sys.stdin.buffer.readline().decode().split()))
isn = lambda n: [sys.stdin.buffer.readline().decode().rstrip() for _ in range(n)]

lcm = lambda x, y: (x * y) // math.gcd(x, y)

MOD = 10 ** 9 + 7
INF = float('inf')


def main():
    if os.getenv("LOCAL"):
        sys.stdin = open("input.txt", "r")

    N, M = il()
    ret = 0
    while M >= 2:
        if N >= 1 and M >= 2:
            ret += 1
            M -= 2
            N -= 1
        if N == 0 and M >= 2:
            N += 1
            M -= 2
    print(ret)


if __name__ == '__main__':
    main()


Fixed submission:
import sys, os, math, bisect, itertools, collections, heapq, queue, copy, array

# from scipy.sparse.csgraph import csgraph_from_dense, floyd_warshall
# from decimal import Decimal
# from collections import defaultdict, deque

sys.setrecursionlimit(10000000)

ii = lambda: int(sys.stdin.buffer.readline().rstrip())
il = lambda: list(map(int, sys.stdin.buffer.readline().split()))
fl = lambda: list(map(float, sys.stdin.buffer.readline().split()))
iln = lambda n: [int(sys.stdin.buffer.readline().rstrip()) for _ in range(n)]

iss = lambda: sys.stdin.buffer.readline().decode().rstrip()
sl = lambda: list(map(str, sys.stdin.buffer.readline().decode().split()))
isn = lambda n: [sys.stdin.buffer.readline().decode().rstrip() for _ in range(n)]

lcm = lambda x, y: (x * y) // math.gcd(x, y)

MOD = 10 ** 9 + 7
INF = float('inf')


def main():
    if os.getenv("LOCAL"):
        sys.stdin = open("input.txt", "r")

    N, M = il()

    ret = 0
    if N * 2 <= M:
        ret += N
        ret += (M - N * 2) // 4
    else:
        ret += M // 2
    print(ret)


if __name__ == '__main__':
    main()