Problem Narrative

You’re on-call for a fintech fraud detection platform processing millions of card swipes per minute. A critical service keeps a fixed-size in-memory buffer of the most recent event IDs to power real-time alerting. During incident mitigation, you need to rotate this buffer efficiently to align “most recent” events with downstream consumers—without allocating extra memory that could increase GC pressure and tail latency.

Task

Implement a function that rotates an integer array nums to the right by k steps.

• Rotation is circular: elements that fall off the end wrap around to the front.
• You must perform the rotation in-place (modify nums directly) using O(1) extra space.

Input / Output

• Input:
  • nums: list[int] — array of event IDs
  • k: int — number of steps to rotate right
• Output:
  • Return the rotated array (even though the operation is in-place, returning it makes testing easier).

Examples

Example 1

Input: nums = [10, 20, 30, 40, 50, 60, 70], k = 3

Output: [50, 60, 70, 10, 20, 30, 40]

Explanation (step-by-step):

• Right-rotate by 3 means the last 3 elements [50, 60, 70] move to the front.
• The remaining prefix [10, 20, 30, 40] shifts right.

Example 2

Input: nums = [-1, -100, 3, 99], k = 2

Output: [3, 99, -1, -100]

Explanation:

• The last 2 elements [3, 99] wrap to the front.

Constraints

• 1 <= nums.length <= 2 * 10^5
• -10^9 <= nums[i] <= 10^9
• 0 <= k <= 10^9

Notes / Clarifications

1. If k is larger than len(nums), it should behave the same as rotating by k % len(nums).
2. If k == 0 or nums has length 1, the array should remain unchanged.
3. Your solution should avoid allocating another array proportional to n.