Description

There are $n(1\leq n\leq 1000)$ steps in front of Hikari. Every $1s$, she can jump upward by $m(1\leq m\leq n)$ steps (she does not stop on the steps in between).

There are $k(k\leq 10)$ special platforms $a_i$ on the steps. When Hikari stops on such a platform, $m$ increases by $1$.

Ask for the time Hikari spends to reach the top of the steps.

Input Format

There are $2$ lines in total.

The first line contains $3$ non-negative integers $n, m, k$.

The second line contains $k$ positive integers. The $i$-th positive integer is $a_i$. It is guaranteed that the input $a_i$ are strictly increasing.

Output Format

There is $1$ line in total. Output $1$ positive integer, the time spent.

10 5 0

2

31 4 2
8 13

6

Hint

Subtasks

For $60\%$ of the testdata, $k = 0$.

For $100\%$ of the testdata, $1\leq m\leq n\leq 1000$, $k\leq 10$.

Source

MtOI2019 Extra Round T1

Problem setter: disangan233.

Translated by ChatGPT 5