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 $n$ $(1 \le n \le 100)$ — the number of benches in the park.

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

Each of the next $n$ lines contains a single integer $a_i$ $(1 \le a_i \le 100)$ — 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.

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.

Samples

4
6
1
1
1
1

3 7

1
10
5

15 15

3
6
1
6
5

6 12

3
7
1
6
5

7 13