<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>

import heapq

class Solution:
    def maxResult(self, nums: List[int], k: int) -> int:
        n = len(nums)
        a = [float('-inf')] * n
    
        a[0] = nums[0]

        # for i in range(n-1):
        #     for j in range(i+1, min(n,i+k+1)):
        #         a[j] = max(a[j], a[i] + nums[j])

        # for i in range(1, n):
        #     a[i] = max(a[max(0, i-k):i]) + nums[i]

        # heap = []
        # heapq.heappush(heap, -a[0])

        # for i in range(1, n):
        #     mx = -heap[0]
        #     a[i] = mx + nums[i]
        #     heapq.heappush(heap, -a[i])
        #     if i >= k:
        #         heap.remove(-a[i-k])
        #         heapq.heapify(heap)
        #     # print(heap)

        mx = a[0]
        mx_index = 0
        for i in range(1, n):
            a[i] = mx + nums[i]
            if a[i] > mx: mx = a[i]; mx_index = i
            if mx_index == i-k: mx = max(a[i-k+1: i+1]); mx_index = i - a[i-k+1:i+1][::-1].index(mx)

        # print(a)

        return a[-1]

618