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.