Can Array be Sorted by Reversing Fixed-Length Subarrays?

You are given an array of integers and an integer k. You are allowed to perform the following operation any number of times: select a contiguous subarray of length exactly k and reverse it. Your task is to determine whether it is possible to sort the entire array in non-decreasing order using these operations.

Consider the following observations:

• If k = 1, no effective operation can be performed, so the array must be already sorted.
• If k is even, it turns out that you can always sort the array.
• If k is odd, then the operation is restricted. In our approach, we check the array in segments of length k (stepping by k) and verify if each segment is already sorted. If every such segment is sorted, the entire array can be sorted; otherwise, it cannot.

The problem can be formally defined as follows:

Determine whether an array nums of length n can be sorted in non-decreasing order by repeatedly reversing any subarray of length k.

Note: All formulas are given in LaTeX format. For example, the condition when k=1 is written as \(k = 1\), and when checking sorted order, we compare with \(\text{sorted}(\text{nums})\).

inputFormat

The first line contains a single integer \(n\) (the number of elements in the array). The second line contains \(n\) space-separated integers representing the array \(nums\). The third line contains a single integer \(k\), the size of the subarray that can be reversed.

outputFormat

Output a single line: True if the array can be sorted using the operations, or False otherwise.

## sample

4
3 1 2 4
2

True

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