You are given a natural number ~K~ and a permutation ~P~ of the numbers ~1, 2, \dots, N~. Since ~P~ is a permutation, it has length ~N~ and each number from ~1~ to ~N~ appears exactly once. You are allowed to swap two elements if their positions are exactly ~K~ apart. In other words, you may swap ~P_i~ and ~P_j~ only if ~|i-j|=K~. Determine if ~P~ can be sorted from least to greatest.

Constraints

~1 \le K < N \le 100~

Subtask 1 [40%]

~1 \le K \le 2~

Subtask 2 [60%]

~1 \le K < 100~

Input Specification

The first line will contain two space-separated integers, ~N~ and ~K~.
The next line will contain ~N~ space-separated integers, ~P_1, P_2, \dots, P_N~.

Output Specification

Output YES if it may be sorted and NO otherwise.

Sample Input 1

5 1
1 4 3 2 5

Sample Output 1

YES

Explanation for Sample 1

Swap ~P_3~ and ~P_4~. The sequence is now 1 4 2 3 5.
Swap ~P_2~ and ~P_3~. The sequence is now 1 2 4 3 5.
Swap ~P_3~ and ~P_4~. The sequence is now 1 2 3 4 5, which is sorted.

Sample Input 2

5 2
5 4 3 2 1

Sample Output 2

YES

Explanation for Sample 2

Swap ~P_2~ and ~P_4~. The sequence is now 5 2 3 4 1.
Swap ~P_1~ and ~P_3~. The sequence is now 3 2 5 4 1.
Swap ~P_3~ and ~P_5~. The sequence is now 3 2 1 4 5.
Swap ~P_1~ and ~P_3~. The sequence is now 1 2 3 4 5, which is sorted.

Sample Input 3

5 3
5 4 3 2 1

Sample Output 3

NO