<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> and an integer <code>k</code>.</p>

<p>You are initially standing at index <code>0</code>. In one move, you can jump at most <code>k</code> steps forward without going outside the boundaries of the array. That is, you can jump from index <code>i</code> to any index in the range <code>[i + 1, min(n - 1, i + k)]</code> <strong>inclusive</strong>.</p>

<p>You want to reach the last index of the array (index <code>n - 1</code>). Your <strong>score</strong> is the <strong>sum</strong> of all <code>nums[j]</code> for each index <code>j</code> you visited in the array.</p>

<p>Return <em>the <strong>maximum score</strong> you can get</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [<u>1</u>,<u>-1</u>,-2,<u>4</u>,-7,<u>3</u>], k = 2
<strong>Output:</strong> 7
<strong>Explanation:</strong> You can choose your jumps forming the subsequence [1,-1,4,3] (underlined above). The sum is 7.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [<u>10</u>,-5,-2,<u>4</u>,0,<u>3</u>], k = 3
<strong>Output:</strong> 17
<strong>Explanation:</strong> You can choose your jumps forming the subsequence [10,4,3] (underlined above). The sum is 17.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,-5,-20,4,-1,3,-6,-3], k = 2
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length, k &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

"""
dp[i] is the max score you can reach starting at index i
* dp[n - 1] = nums[n - 1]
* Want to find dp[0]
* dp[i] = nums[i] + max(dp[j] for j in range(i + 1, i + k)) 
"""
class Solution:
    def maxResult(self, nums: List[int], k: int) -> int:
        N = len(nums)
        dp = deque([0] * (k + 1))
        dp[0] = nums[-1]
        rolling_max = deque([N - 1])
        for i in range(N - 2, -1, -1):
            if rolling_max and rolling_max[0] - i > k:
                rolling_max.popleft()
            dp.pop()
            dp.appendleft(0)
            dp[0] = nums[i] + dp[rolling_max[0] - i]
            while rolling_max and dp[0] >= dp[rolling_max[-1] - i]:
                rolling_max.pop()
            rolling_max.append(i)
        return dp[0]
30900