<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>

class Solution:
    def maxResult(self, nums: List[int], k: int) -> int:

        dp=[float('-inf')]*len(nums)
        dp[0]=nums[0]

        queue=deque()
        queue.append(0)

        for i in range(1,len(nums)):

            dp[i]= nums[i]+dp[queue[0]]
            while queue and dp[i]>dp[queue[-1]]:
                queue.pop()
           
            queue.append(i)

            if i-queue[0]==k:
                queue.popleft()
        return dp[-1]



        # for i in range(1,len(nums)):

        #     dp[i]= nums[i]+dp[queue[0]]

        #     while queue and dp[i]>dp[queue[-1]]:
        #         queue.pop()
        #     queue.append(i)

        #     if i-queue[0]==k:
        #         queue.popleft()
        # return dp[-1]





























        # dp=[float('-inf')]*len(nums)

        # dp[0]=nums[0]

        # for i in range(len(nums)):
        #     for j in range(1,k+1): 
        #         if i-j>=0:
        #             dp[i]= max(dp[i], dp[i-j]+nums[i])
        # return dp[-1]

        dp=[float('-inf')]*len(nums)
        dp[0]=nums[0]
        queue=deque()
        queue.append(0)

        for i in range(1,len(nums)):
            dp[i]= dp[queue[0]] +nums[i]

            if i-queue[0]==k:
                queue.popleft()
            
            while queue and dp[queue[-1]] < dp[i]:
                queue.pop()
            queue.append(i)
        return dp[-1]




























        n=len(nums)
        dp= [0]*len(nums)
        dp[0]=nums[0]
        queue=deque()
        queue.append(0)

        for i in range(1,len(nums)):
            dp[i]=nums[i]+dp[queue[0]]

            if queue[0]<=i-k:
                queue.popleft()
            
            while queue and dp[i]> dp[queue[-1]]:
                queue.pop()
            queue.append(i)
        return dp[-1]








                
    

        # n=len(nums)
        # dp=[float('-inf')]*n
        # dp[0]=nums[0]
        # for i in range(n):
        #     for j in range(1,k+1):
        #         if i+j<len(nums):
        #             dp[i+j]= max(dp[i+j], nums[i+j]+ dp[i]) 
        # return dp[-1]


        # n = len(nums)
        # deq = deque([])
        # deq.append(0)
        # dp = [0] * n
        # dp[0] = nums[0]
        
        # for i in range(1,n):
        #     dp[i]=nums[i]+dp[deq[0]]

        #     if deq[0]<= i-k:
        #         deq.popleft()
        #     while deq and dp[i]>dp[deq[-1]]:
        #         deq.pop()
        #     deq.append(i)
        # return dp[-1]




        
709