K-Sort

You are given a permutation $A=[A_0, A_1, \dots, A_{N-1}]$ of length $N$. A permutation of length $N$ is a sequence in which every integer from $0$ to $N-1$ appears exactly once.

A positive integer $K$ is also given. You may perform the following operation as many times as you like.

• For any $i$ ($0 \leq i < N$), swap the values of $A_i$ and $A_{(i+K) \bmod N}$.

Determine whether $A$ can be sorted into ascending order using this operation. See the hint for the definition of $\bmod$.

The first line contains the length $N$ and the positive integer $K$, separated by a space. ($1 \leq K \leq N \leq 10^{6}$)

The second line contains the elements $A_0, A_1, \dots, A_{N-1}$, separated by spaces. Each integer from $0$ to $N-1$ appears exactly once.

Print YES if $A$ can be sorted into ascending order by repeating the operation, otherwise print NO.

$\bmod$ is the remainder operation. $a \bmod b$ is the remainder when $a$ is divided by $b$. For example, $5 \bmod 3 = 2$.