2551 - Put Marbles in Bags.

Hard

You have k bags. You are given a 0-indexed integer array weights where weights[i] is the weight of the <code>i^th</code> 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 <code>i^th</code> marble and <code>j^th</code> marble are in a bag, then all marbles with an index between the <code>i^th</code> and <code>j^th</code> 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.

Example 1:

Input: weights = 1,3,5,1, k = 2

Output: 4

Explanation:

The distribution 1,3,5,1 results in the minimal score of (1+1) + (3+1) = 6.

The distribution 1,3,5,1, results in the maximal score of (1+3) + (5+1) = 10.

Thus, we return their difference 10 - 6 = 4.

Example 2:

Input: weights = 1, 3, k = 2

Output: 0

Explanation:

The only distribution possible is 1,3.

Since both the maximal and minimal score are the same, we return 0.

Constraints:

• <code>1 <= k <= weights.length <= 10⁵</code>

• <code>1 <= weightsi<= 10⁹</code>