## USACO 2017 February Contest, Silver

## Problem 2. Why Did the Cow Cross the Road II

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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.

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#### 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