C. Linear Maze
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

There is a maze consisting of n rooms. From the i-th room, you can move to room i + 1 (but not the other way).

The entrance to the maze is in room 1, and moving from the n-th room leads to the exit.

But what is the point of a maze if it can be traversed directly?

Therefore, the creators of the maze invented branch rooms — if you visit such a room on the 1-st, 3-rd, 5-th, etc. visit (that is, on each odd visit) — then the transition from it will lead back to room 1 instead of the next numbered room (or the exit).

It is known that rooms r1, r2, ..., rk are branch rooms.

Output the total number of rooms that need to be visited to exit the maze.

Input

The first line contains two integers n and k (1 ≤ n ≤ 30,  0 ≤ k ≤ n) — the total number of rooms in the maze and the number of branch rooms, respectively.

The next line contains k integers r1, r2, ..., rk (1 ≤ r1 < r2 < ... < rk ≤ n) — the numbers of the branch rooms.

Output

In a single line, output an integer — the total number of rooms that need to be visited to exit the maze.

Example
Input
5 2
2 4
Output
13
Note

First test example

The sequence of visited rooms will be as follows:

(1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 5), after which the exit follows.

A total of 13 rooms were visited.