Buggy python submission (verdict: Time Limit Exceeded):
def main():

    N_machi, K_teleport = map(int, input().split())
    to_teleport = list(map(int, input().split()))

    def find_double_town():
        visited_city = [0]
        first_twice = N_machi
        
        next_city = 0
        
        for i in range(N_machi):
            next_city = to_teleport[next_city] - 1
            visited_city.append(next_city)
            if (len(visited_city) != len(set(visited_city))):
                first_twice = i + 1
                break
        
        return (next_city, first_twice)


    index_city, second_visit = find_double_town()
    if (index_city == 0):
        first_visit = 0
    else:
        next_city = 0        
        for i in range(N_machi):
            next_city = to_teleport[next_city] - 1
            
            if (next_city == index_city):
                first_visit = i + 1
                break

    if (K_teleport >= first_visit):
        mod = (K_teleport - first_visit) % (second_visit - first_visit)
        next_city = index_city
        
    else:
        mod = K_teleport
        next_city = 0

    for i in range(mod):
        next_city = to_teleport[next_city] - 1

    ans = next_city + 1

    print(ans)
    # print(first_visit,second_visit)


if __name__ == '__main__':
    main()

Fixed submission:
def main():

    N_machi, K_teleport = map(int, input().split())
    to_teleport = list(map(int, input().split()))

    visited_city = [1]
    order = [-1 for i in range(N_machi + 1)]
    order[1] = 0
    next_city = 1
    
    for i in range(N_machi):
        next_city = to_teleport[next_city - 1]
        tmp = order[next_city]
        
        if (tmp == -1):
            visited_city.append(next_city)
            order[next_city] = i + 1
        else:
            break
    
    first = order[next_city]
    len_loop = len(visited_city) - first
    
    if (K_teleport < first):
        ans = visited_city[K_teleport]
    else:
        mod = (K_teleport - first) % len_loop
        ans = visited_city[first + mod]
    
    print(ans)
        

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
def main():

    N_machi, K_teleport = map(int, input().split())
    to_teleport = list(map(int, input().split()))

    def find_double_town():
        visited_city = [0]
        first_twice = N_machi
        
        next_city = 0
        
        for i in range(N_machi):
            next_city = to_teleport[next_city] - 1
            visited_city.append(next_city)
            if (len(visited_city) != len(set(visited_city))):
                first_twice = i + 1
                break
        
        return (next_city, first_twice)


    index_city, second_visit = find_double_town()
    if (index_city == 0):
        first_visit = 0
    else:
        next_city = 0        
        for i in range(N_machi):
            next_city = to_teleport[next_city] - 1
            
            if (next_city == index_city):
                first_visit = i + 1
                break

    if (K_teleport >= first_visit):
        mod = (K_teleport - first_visit) % (second_visit - first_visit)
        next_city = index_city
        
    else:
        mod = K_teleport
        next_city = 0

    for i in range(mod):
        next_city = to_teleport[next_city] - 1

    ans = next_city + 1

    print(ans)


if __name__ == '__main__':
    main()

Fixed submission:
def main():

    N_machi, K_teleport = map(int, input().split())
    to_teleport = list(map(int, input().split()))

    visited_city = [1]
    order = [-1 for i in range(N_machi + 1)]
    order[1] = 0
    next_city = 1
    
    for i in range(N_machi):
        next_city = to_teleport[next_city - 1]
        tmp = order[next_city]
        
        if (tmp == -1):
            visited_city.append(next_city)
            order[next_city] = i + 1
        else:
            break
    
    first = order[next_city]
    len_loop = len(visited_city) - first
    
    if (K_teleport < first):
        ans = visited_city[K_teleport]
    else:
        mod = (K_teleport - first) % len_loop
        ans = visited_city[first + mod]
    
    print(ans)
        

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
def main():

    N_ko, K_kai = map(int, input().split())
    teleport = list(map(int, input().split()))

    index = 0
    ctr = 0
    before_ctr = 0

    Visited = []
    Visited.append(ctr)

    for i in range(N_ko + 1):

        ctr += 1
        index = teleport[index] - 1
        Visited.append(index)
        
        if (index == 0):
            FLAG = 1
            break

        if (len(Visited) != len(set(Visited))):
            FLAG = 0
            break


    if (FLAG):
        mod = K_kai % ctr
        city = 0

        for i in range(mod):
            city = teleport[city] - 1

        ans = city + 1

    # else:
    #     cnt = 0
    #     before_ctr = 0

    #     for i in range(N_ko + 1):
    #         cnt += 1
    #         current_index = teleport[index] - 1
            
    #         if (current_index == index):
    #             before_ctr = cnt
    #             break
        
    #     if (K_kai < ctr):
    #         city = 0
            
    #         for i in range(K_kai):
    #             city = teleport[city] - 1

    #         ans = city + 1

    #     else:
    #         ans = (K_kai - before_ctr) % (ctr - before_ctr)
    #         ans += 1
            

    print(ans)


if __name__ == '__main__':
    main()

Fixed submission:
def main():

    N_machi, K_teleport = map(int, input().split())
    to_teleport = list(map(int, input().split()))

    visited_city = [1]
    order = [-1 for i in range(N_machi + 1)]
    order[1] = 0
    next_city = 1
    
    for i in range(N_machi):
        next_city = to_teleport[next_city - 1]
        tmp = order[next_city]
        
        if (tmp == -1):
            visited_city.append(next_city)
            order[next_city] = i + 1
        else:
            break
    
    first = order[next_city]
    len_loop = len(visited_city) - first
    
    if (K_teleport < first):
        ans = visited_city[K_teleport]
    else:
        mod = (K_teleport - first) % len_loop
        ans = visited_city[first + mod]
    
    print(ans)
        

if __name__ == '__main__':
    main()