I am asking this question for another person btw.

I know how to find LIS in $$$O(n \log n)$$$ with binary search and is pretty well known. I am trying to find the Maximum Sum Increasing Subsequence in $$$O(n \log n)$$$. This can be solved using a BIT or a segtree, but is there an approach with binary search like LIS? https://www.geeksforgeeks.org/maximum-sum-increasing-subsequence-dp-14/.