Problem 2. Why Did the Cow Cross the Road II

USACO 2017 February Contest, Silver

The long road through Farmer John's farm has $N$ crosswalks across it, conveniently numbered $1 \ldots N$ ($1 \leq N \leq 100,000$). To allow cows to cross at these crosswalks, FJ installs electric crossing signals, which light up with a green cow icon when it is ok for the cow to cross, and red otherwise. Unfortunately, a large electrical storm has damaged some of his signals. Given a list of the damaged signals, please compute the minimum number of signals that FJ needs to repair in order for there to exist some contiguous block of at least $K$ working signals.

INPUT FORMAT (file maxcross.in):

The first line of input contains $N$, $K$, and $B$ ($1 \leq B, K \leq N$). The next $B$ lines each describe the ID number of a broken signal.

OUTPUT FORMAT (file maxcross.out):

Please compute the minimum number of signals that need to be repaired in order for there to be a contiguous block of $K$ working signals somewhere along the road.

SAMPLE INPUT:

10 6 5
2
10
1
5
9

SAMPLE OUTPUT:

1

Problem credits: Brian Dean