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 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

A. Presents

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe Hedgehog likes to give presents to his friend, but no less he likes to receive them.

Having received another present today, the Hedgehog suddenly understood that he has no place to put it as there was no room left on the special shelf in the cupboard. He will have to choose another shelf, but which one should he choose, how large should it be?

In order to get to know this, the Hedgehog asks you to write him a program that will count the estimated number of presents that he will receive during the following *N* days. Besides, he is guided by the principle:

- on each holiday day the Hedgehog will necessarily receive a present,
- he receives presents at least every
*K*days (i.e., if he received a present on the*i*-th day, he will receive the next present no later than on the*i*+*K*-th day).

For the given *N* and *K*, as well as the list of holidays among the following *N* days count the minimal number of presents that could be given to the Hedgehog. The number of today's day is zero, and you should regard today's present as already given (i.e., you shouldn't count it in the answer).

Input

The first line contains integers *N* and *K* (1 ≤ *N* ≤ 365, 1 ≤ *K* ≤ *N*).

The second line contains a number *C* which represents the number of holidays (0 ≤ *C* ≤ *N*). Then in the same line follow *C* numbers ranging from 1 to *N* which are the numbers of holiday days. The numbers are given in the increasing order, without repeating numbers among them.

Output

Print a single number — the minimal number of presents the Hedgehog will receive over the following *N* days.

Examples

Input

5 2

1 3

Output

3

Input

10 1

3 6 7 8

Output

10

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/07/2020 02:12:19 (i2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|