Leapcow

Cows like to bury each other in sand at the beach. On this beach, cows are buried only at integer coordinates of a one-dimensional number line. Bessie wants to travel from one end of the beach (coordinate 0) to the other end (coordinate $E$) without stepping on any buried cow.

$5 \le E \le 40{,}000$

Bessie travels only by leaps, and each leap has a length from 1 to $L$.

$3 \le L \le 50$

You are given the locations (from 1 to $E-1$) of the $B$ buried cows, where $1 \le B \le 500$. Find the least number of leaps Bessie needs to get from one end to the other. An answer is guaranteed to exist.

The first line contains three space-separated integers $E$, $L$, and $B$. Each of the next $B$ lines contains one integer, the coordinate of a buried cow.

Print a single integer: the smallest number of legal leaps Bessie needs to reach coordinate $E$.

The diagram shows the beach and the leaps. The letter c marks a cow.

# # c c # #   <--- cow denoted by 'c'
0 1 2 3 4 5   <--- location numbers
  1     2 3   <--- where leaps 1, 2, and 3 end