Please solve the programming task below using a self-contained code snippet in a markdown code block.

You are given a 0-indexed integer array nums and a positive integer k.
We call an index i k-big if the following conditions are satisfied:

There exist at least k different indices idx1 such that idx1 < i and nums[idx1] < nums[i].
There exist at least k different indices idx2 such that idx2 > i and nums[idx2] < nums[i].

Return the number of k-big indices.
 
Please complete the following python code precisely:
```python
class Solution:
    def kBigIndices(self, nums: List[int], k: int) -> int:
```