There are n benches in the Berland Central park. It is known that a_i people are currently sitting on the i-th bench. Another m people are coming to the park and each of them is going to have a seat on some bench out of n available.

Let k be the maximum number of people sitting on one bench after additional m people came to the park. Calculate the minimum possible k and the maximum possible k.

Nobody leaves the taken seat during the whole process.

Input

The first line contains a single integer n (1 ≤ n ≤ 100) — the number of benches in the park.

The second line contains a single integer m (1 ≤ m ≤ 10 000) — the number of people additionally coming to the park.

Each of the next n lines contains a single integer a_i (1 ≤ a_i ≤ 100) — the initial number of people on the i-th bench.

Output

Print the minimum possible k and the maximum possible k, where k is the maximum number of people sitting on one bench after additional m people came to the park.

Examples

Input

4
6
1
1
1
1


Output

3 7


Input

1
10
5


Output

15 15


Input

3
6
1
6
5


Output

6 12


Input

3
7
1
6
5


Output

7 13

Note

In the first example, each of four benches is occupied by a single person. The minimum k is 3. For example, it is possible to achieve if two newcomers occupy the first bench, one occupies the second bench, one occupies the third bench, and two remaining — the fourth bench. The maximum k is 7. That requires all six new people to occupy the same bench.

The second example has its minimum k equal to 15 and maximum k equal to 15, as there is just a single bench in the park and all 10 people will occupy it.
from sys import stdin, stdout
import cProfile,math

printHeap = str()
test = False
memory_constrained = False


def display(string_to_print):
    stdout.write(str(string_to_print) + "\n")


def test_print(output):
    if test:
        stdout.write(str(output) + "\n")


def display_list(list1, sep=" "):
    stdout.write(sep.join(map(str, list1)) + "\n")


def get_int():
    return int(stdin.readline().strip())


def get_tuple():
    return map(int, stdin.readline().split())


def get_list():
    return list(map(int, stdin.readline().split()))


memory = dict()


def clear_cache():
    global memory
    memory = dict()


def cached_fn(fn, *args):
    global memory
    if args in memory:
        return memory[args]
    else:
        result = fn(*args)
        memory[args] = result
        return result


# ----------------------------------------------------------------------------------- MAIN PROGRAM

from collections import Counter
def main():
    n = get_int()
    m = get_int()
    li = list()
    for i in range(n):
        li.append(get_int())
    mini = max(li) if sum(li)+m <= max(li)*n else math.ceil((sum(li)+m)/n)
    print(mini, max(li)+m)





















# --------------------------------------------------------------------------------------------- END


cProfile.run('main()') if test else main()