Maximize the Score of Bounded Forward Jumps

### Problem Start at index 0 of `nums` and finish at its final index. Each jump advances between 1 and `k` positions without leaving the array. Your score includes the values at every visited index, including the start and finish. Return the greatest possible score. ```cpp class Solution { public: int maxResult(vector<int>& nums, int k); }; ``` ### Examples **Example 1:** ```text nums = [2,-3,4,-2,5], k = 2 Output: 11 Explanation: Visit indices 0, 2, and 4. ``` **Example 2:** ```text nums = [-2,-5,-1], k = 1 Output: -8 Explanation: Every index must be visited when the maximum jump is one. ``` ### Constraints - Both `nums.length` and `k` lie in `[1,10^5]`. - `-10^4 <= nums[i] <= 10^4`. ### Clarifying Questions Forward steps cannot have length zero. Negative values are allowed and the route must still reach the last index. ```hint Inspect the structure What must a valid route include even when some visited values are negative? ``` ### Reasoning checkpoints - Include both endpoints and use only forward jumps of allowed length. - Prove the maximum score even when every available continuation has a negative contribution. ### Optional extensions How does a heap-based sliding maximum compare with a monotone deque here?