```python
def kth_distinct(values: list[int], k: int) -> int:
    if not values:
        raise ValueError("Input list cannot be empty.")
    if not isinstance(k, int) or k <= 0:
        raise ValueError("Rank must be a positive integer.")
    distinct_values = sorted(set(values))
    if k > len(distinct_values):
        raise ValueError("Rank exceeds the count of distinct values.")
    return distinct_values[k - 1]
```