number of permutation with k inversions

Question

We are given two numbers N and K.

N <= 10^9.

K<=min{1000,(N*(N-1))/2}

We need to find numbers of permutations of ( 1 to N ) such that inversions are exactly K.

If N was <= 10^3. It would be a simple Dynamic programming question.

https://www.geeksforgeeks.org/number-of-permutation-with-k-inversions/

can we optimize it?