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.

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.

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.

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.

见题面 Input 部分

见题面 Output 部分