Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. Airport

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLolek and Bolek are about to travel abroad by plane. The local airport has a special "Choose Your Plane" offer. The offer's conditions are as follows:

- it is up to a passenger to choose a plane to fly on;
- if the chosen plane has
*x*(*x*> 0) empty seats at the given moment, then the ticket for such a plane costs*x*zlotys (units of Polish currency).

The only ticket office of the airport already has a queue of *n* passengers in front of it. Lolek and Bolek have not stood in the queue yet, but they are already wondering what is the maximum and the minimum number of zlotys the airport administration can earn if all *n* passengers buy tickets according to the conditions of this offer?

The passengers buy tickets in turn, the first person in the queue goes first, then goes the second one, and so on up to *n*-th person.

Input

The first line contains two integers *n* and *m* (1 ≤ *n*, *m* ≤ 1000) — the number of passengers in the queue and the number of planes in the airport, correspondingly. The next line contains *m* integers *a*_{1}, *a*_{2}, ..., *a*_{m} (1 ≤ *a*_{i} ≤ 1000) — *a*_{i} stands for the number of empty seats in the *i*-th plane before the ticket office starts selling tickets.

The numbers in the lines are separated by a space. It is guaranteed that there are at least *n* empty seats in total.

Output

Print two integers — the maximum and the minimum number of zlotys that the airport administration can earn, correspondingly.

Examples

Input

4 3

2 1 1

Output

5 5

Input

4 3

2 2 2

Output

7 6

Note

In the first test sample the number of passengers is equal to the number of empty seats, so regardless of the way the planes are chosen, the administration will earn the same sum.

In the second sample the sum is maximized if the 1-st person in the queue buys a ticket to the 1-st plane, the 2-nd person — to the 2-nd plane, the 3-rd person — to the 3-rd plane, the 4-th person — to the 1-st plane. The sum is minimized if the 1-st person in the queue buys a ticket to the 1-st plane, the 2-nd person — to the 1-st plane, the 3-rd person — to the 2-nd plane, the 4-th person — to the 2-nd plane.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/20/2017 18:29:28 (c2).

Desktop version, switch to mobile version.

User lists

Name |
---|