#AT2191. C - K Swap
C - K Swap
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C - K Swap
Score : $300$ points
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:
Output
If it is possible to sort $A$ in ascending order, print Yes
; otherwise, print No
.
5 2
3 4 1 3 4
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 $(1,3,3,4,4)$.
5 3
3 4 1 3 4
No
7 5
1 2 3 4 5 5 10
Yes
No operations may be needed.