Maximum Two-Fragment Sum

You are given an integer array nums and two integers k and l.

Choose two contiguous fragments of nums: one of length k and one of length l. The two fragments may overlap (they may even occupy the same positions).

The chosen fragments determine a total:

• an element covered by exactly one fragment adds its value;
• an element covered by both fragments adds its negated value;
• an element covered by neither fragment adds nothing.

Return the maximum total over all placements of the two fragments.

Examples

Example 1

Input: nums = [1, 3, -4, 2, -2], k = 3, l = 2
Output: 10
Explanation: Take the length-3 fragment at indices 0-2 and the length-2 fragment
at indices 2-3. Index 2 is covered by both fragments, so -4 contributes +4.
Total = 1 + 3 + 4 + 2 = 10.

Example 2

Input: nums = [-3], k = 1, l = 1
Output: 3
Explanation: Both fragments must cover the single element, which is therefore
negated: -(-3) = 3.