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

You have k bags. You are given a 0-indexed integer array weights where weights[i] is the weight of the ith marble. You are also given the integer k.
Divide the marbles into the k bags according to the following rules:

No bag is empty.
If the ith marble and jth marble are in a bag, then all marbles with an index between the ith and jth indices should also be in that same bag.
If a bag consists of all the marbles with an index from i to j inclusively, then the cost of the bag is weights[i] + weights[j].

The score after distributing the marbles is the sum of the costs of all the k bags.
Return the difference between the maximum and minimum scores among marble distributions.
 
Please complete the following python code precisely:
```python
class Solution:
    def putMarbles(self, weights: List[int], k: int) -> int:
```