Solution: Find the K-Sum of an Array

Explore how to determine the kth largest subsequence sum in an array by transforming the problem into finding losses and using a min heap for efficient computation. Understand the approach to sum positive elements, convert negatives, sort, and systematically explore smallest losses to solve the problem within time and space constraints.

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Statement
Solution
- Time complexity
- Space complexity

Statement

You are given an integer array, nums, and a positive integer k. Your task is to determine and return the $k^{th}$ largest possible sum among all subsequences of the array. A subsequence is formed by deleting no or more elements from the array without changing the order of the remaining elements. The sum of a subsequence is the total of its elements.

Remember: For valid subsequences:
The empty subsequence is valid, and its sum is considered $0$ .
Duplicate subsequence sums are allowed and counted separately when determining the $k^{th}$ largest.

Constraints:

$n ==$ nums.length
$1 \leq$ n $\leq 10^3$
$-10^3 \leq$ nums[i] ...