Close equal numbers P63257

Statement

Given an integer number $k$ and $n$ numbers $x_1, \dots x_n$ , are there at least two equal numbers at distance at most $k$ ? Consider the sequence of $x_i$ ’s circularly, that is, assume that $x_1$ is to the right of $x_n$ .

Input

Input consists of several cases, each with $k$ and $n$ , followed by $x_1, \dots x_n$ . You can assume $1 \le k \le n/2$ , $2 \le n \le 10^5$ , and that each $x_i$ is an integer number between 0 and $10^9$ .

Output

For every case, print “yes” if there is at least a pair of $x_i$ ’s with the required condition, and print “no” otherwise.

Public test cases

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

Information

Author: Javier Nistal
Language: English
Official solutions: C++
User solutions: C++