Given an integer number k and n numbers x1, … xn, are there at least two equal numbers at distance at most k? Consider the sequence of xi’s circularly, that is, assume that x1 is to the right of xn.
Input
Input consists of several cases, each with k and n, followed by x1, … xn. You can assume 1 ≤ k ≤ n/2, 2 ≤ n ≤ 105, and that each xi is an integer number between 0 and 109.
Output
For every case, print “yes” if there is at least a pair of xi’s with the required condition, and print “no” otherwise.
Input
4 8 10 42 23 33 12 42 17 18 3 8 10 42 23 33 12 42 17 18 4 7 10 42 23 33 12 42 17 3 7 10 42 23 33 12 42 17
Output
yes no yes yes