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.
# IMPORTS---------------------------------------------------------------------#
from __future__ import division, print_function

import math
import operator as op
import random
#from atexit import register
from collections import Counter, defaultdict, deque
from fractions import Fraction, gcd
#from io import BytesIO
#from decimal import Decimal, getcontext
from itertools import combinations, ifilter, imap, izip, permutations, product
from Queue import PriorityQueue, Queue
from string import ascii_lowercase, ascii_uppercase
from sys import __stdout__, setrecursionlimit, stdin, stdout


# PYTHON3---------------------------------------------------------------------#
range = xrange
filter = ifilter
map = imap
zip = izip


# SETTINGS--------------------------------------------------------------------#
#getcontext().prec = 100
#setrecursionlimit(100000)


# CONSTANTS-------------------------------------------------------------------#
MOD = 1000000007
INF = float('+inf')


# FASTIO----------------------------------------------------------------------#
#stdout = BytesIO()
#register(lambda: __stdout__.write(stdout.getvalue()))
#stdin = BytesIO(stdin.read())


# IO--------------------------------------------------------------------------#
input = lambda: stdin.readline().rstrip()
print = lambda *args: stdout.write(' '.join(str(x) for x in args) + '\n')
#flush = stdout.flush()


# MAIN------------------------------------------------------------------------#
def main():
    n = int(input())
    m = int(input())
    a = []
    for i in range(n):
        a.append(int(input()))

    print(int(max(math.ceil((sum(a) + m ) / n), max(a))), max(a) + m)


if __name__ == '__main__':
    main()
