human
I found an interesting problem on https://leetcode.com/problems/constrained-subsequence-sum/:
Given an integer array nums and an integer k, return the maximum sum of a non-empty subsequence of that array such that for every two consecutive integers in the subsequence, nums[i] and nums[j], where i < j, the condition j - i <= k is satisfied.
A subsequence of an array is obtained by deleting some number of elements (can be zero) from the array, leaving the remaining elements in their original order.
 
Example 1:
Input: nums = [10,2,-10,5,20], k = 2
Output: 37
Explanation: The subsequence is [10, 2, 5, 20].

Example 2:
Input: nums = [-1,-2,-3], k = 1
Output: -1
Explanation: The subsequence must be non-empty, so we choose the largest number.

Example 3:
Input: nums = [10,-2,-10,-5,20], k = 2
Output: 23
Explanation: The subsequence is [10, -2, -5, 20].

 
Constraints:

1 <= k <= nums.length <= 10^5
-10^4 <= nums[i] <= 10^4

I tried it in Python, but could not do it. Can you solve it?

 Give me a the Python program you requested?
assistant
#Here is the Python program you requested.

class Solution:
    def constrainedSubsetSum(self, nums: List[int], k: int) -> int:
        pq = [(-nums[0], 0)]
        res = nums[0]
        for i in range(1, len(nums)):
            rm = i - k - 1
            while pq[0][1] <= rm:
                heapq.heappop(pq)
            cur = max(-pq[0][0], 0) + nums[i]
            res = max(res, cur)
            heapq.heappush(pq, (-cur, i))
        return res