There is a circular list of non-zero integers called nums. Each number in the list tells you how many steps to move forward or backward from your current position:

• If nums[i] is positive, move nums[i] steps forward.

• If nums[i] is negative, move nums[i] steps backward.

As the list is circular:

• Moving forward from the last element takes you back to the first element.

• Moving backward from the first element takes you to the last element.

A cycle in this list means:

1. You keep moving according to the numbers, and you end up repeating a sequence of indexes.

2. All numbers in the cycle have the same sign (either all positive or all negative).

3. The cycle length is greater than 1 (it involves at least two indexes).

Return true if such a cycle exists in the list or false otherwise.