PeterWang needs help with virus extermination! There are $Q$ viruses which are in capsules numbered from $1$ to $N$, however not all capsules have a virus in them. PeterWang has an extermination ray that can exterminate capsules in the range $[l,r]$ (This includes ones that contain a virus and ones that do not). However, he can only use the ray up to $M$ times.

Since capsules are quite expensive, can you tell PeterWang what is the minimum number of capsules that he has to destroy to exterminate the virus?

Input Specification

First line, 3 integers $N$, $M$, $Q$, denoting the number of capsules, maximum number of times PeterWang can use the ray, and the number of viruses, respectively.

Next $Q$ lines, the capsule number $v_i$, denoting where the $i^{\text{th}}$ virus resides in $(1\le v_i\le N)$.

Output Specification

Output one integer, the minimum number of capsules that need to be destroyed in order to exterminate the virus.

Subtasks

For all subtasks:

$1\le Q\le N\le {10}^6$

$1\le M\le {10}^3$

Subtask 1 [30%]

$1\le Q\le N\le {10}^3$

$1\le M\le 100$

Subtask 2 [70%]

No additional constraints.

Sample Input

10 2 5
3
4
5
7
10

Sample Output

6

Sample Explanation

PeterWang can use the ray on capsules $[3,7]$ and then on capsule $10$, which will result in $5+1=6$ total capsules destroyed, including the capsules that did not have the virus in them.