Problem Statement

We have a sequence of length $N$: $A=(a_1,\\ldots,a_N)$. Additionally, you are given an integer $K$.

You can perform the following operation zero or more times.

• Choose an integer $i$ such that $1 \\leq i \\leq N-K$, then swap the values of $a_i$ and $a_{i+K}$.

Determine whether it is possible to sort $A$ in ascending order.

Constraints

• $2 \\leq N \\leq 2 \\times 10^5$
• $1 \\leq K \\leq N-1$
• $1 \\leq a_i \\leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$ $a_1$ $\\ldots$ $a_N$

Output

If it is possible to sort $A$ in ascending order, print Yes; otherwise, print No.

Sample Input 1

5 2
3 4 1 3 4

Sample Output 1

Yes

The following sequence of operations sorts $A$ in ascending order.

• Choose $i=1$ to swap the values of $a_1$ and $a_3$. $A$ is now $(1,4,3,3,4)$.
• Choose $i=2$ to swap the values of $a_2$ and $a_4$. $A$ is now $(1,3,3,4,4)$.

Sample Input 2

5 3
3 4 1 3 4

Sample Output 2

No

Sample Input 3

7 5
1 2 3 4 5 5 10

Sample Output 3

Yes

No operations may be needed.