The long road through Farmer John's farm has n crosswalks across it, conveniently numbered 1 .. n. 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

The first line contains n (1 ≤ n ≤ 105), k and b (1 ≤ b, k ≤ n). The next b lines each describe the ID number of a broken signal.

Output

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.