Problem: Given an array of length $$$n$$$, find the number of increasing subsequences of length $$$k$$$, modulo $$$10^{9} + 7$$$.

I know that it can be done via the following DP, which can be optimized to $$$\mathcal O(nklogn)$$$ using a BIT or segment tree:

But could it be further optimized? I can't seem to find any mentions of a faster algorithm online.