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You are given a **0-indexed** integer array `nums` and an integer `k`. You are initially standing at index `0`. In one move, you can jump at most `k` steps forward without going outside the boundaries of the array. That is, you can jump from index `i` to any index in the range `[i + 1, min(n - 1, i + k)]` **inclusive**. You want to reach the last index of the array (index `n - 1`). Your **score** is the **sum** of all `nums[j]` for each index `j` you visited in the array. Return the **maximum score** you can get.
Example 1
Input: nums = [1,-1,-2,4,-7,3], k = 2
Output: 7
Explanation: Visit indices 0,1,3,5 → 1 + (-1) + 4 + 3 = 7 (jumps of size <= 2).
Example 2
Input: nums = [10,-5,-2,4,0,3], k = 3
Output: 17
Explanation: Best route collects 10 + 4 + 3 = 17 using jumps of at most 3.
Example 3
Input: nums = [1,-5,-20,4,-1,3,-6,-3], k = 2
Output: 0
Explanation: The best route is 0 → 1 → 3 → 5 → 7, collecting 1 + (-5) + 4 + 3 + (-3) = 0. Skipping -5 would mean landing on -20, and the last index (-3) must always be counted.
dp[i] = best score to reach i = nums[i] + max(dp[i-k..i-1]). The inner max over a sliding window of size k is the classic monotonic-deque trick: keep indices whose dp is decreasing, drop ones that fell out of the window, and the front is always the window maximum.
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