Put Marbles in Bags

You are given an integer array weights where each element represents the weight of a marble, and an integer k representing how many bags we must divide the marbles into.

The marbles must be divided using these rules:

1. Every bag must contain at least one marble.

2. Marbles placed in a bag must form a continuous segment in the original array.
   (If marbles at positions i and j are in the same bag, then all marbles from i to j must also be in that bag.)

3. Cost of a bag that contains marbles from index i to j is calculated as:

   weights[i] + weights[j]

4. The total score of a distribution is the sum of costs of all k bags.

Your task is to compute the difference between:

• The maximum possible total score,

• The minimum possible total score.

Return this difference.