You are playing a game involving a circular array of non-zero integers `nums`. Each `nums[i]` denotes the number of indices forward/backward you must move if you are located at index `i`:

- If `nums[i]` is positive, move `nums[i]` steps forward, and
- If `nums[i]` is negative, move `nums[i]` steps backward.

Since the array is circular, you may assume that moving forward from the last element puts you on the first element, and moving backwards from the first element puts you on the last element.

A cycle in the array consists of a sequence of indices `seq` of length `k` where:

- Following the movement rules above results in the repeating index sequence `seq[0] -> seq[1] -> ... -> seq[k - 1] -> seq[0] -> ...`
- Every `nums[seq[j]]` is either all positive or all negative.
- `k > 1`

Return `true` if there is a cycle in `nums`, or `false` otherwise.

Example 1:

    Input: nums = [2,-1,1,2,2]
    Output: true
    Explanation:
    There is a cycle from index 0 -> 2 -> 3 -> 0 -> ...
    The cycle's length is 3.

Example 2:

    Input: nums = [-1,2]
    Output: false
    Explanation:
    The sequence from index 1 -> 1 -> 1 -> ... is not a cycle because the sequence's length is 1.
    By definition the sequence's length must be strictly greater than 1 to be a cycle.

Example 3:

    Input: nums = [-2,1,-1,-2,-2]
    Output: false
    Explanation:
    The sequence from index 1 -> 2 -> 1 -> ... is not a cycle because nums[1] is positive, but nums[2] is negative.
    Every nums[seq[j]] must be either all positive or all negative.

Constraints:

- `1 <= nums.length <= 5000`
- `-1000 <= nums[i] <= 1000`
- `nums[i] != 0`

Follow up: Could you solve it in `O(n)` time complexity and `O(1)` extra space complexity?