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