Permutations with K Inversions

Given two non-negative integers N and K, return the number of permutations of length N with exactly K inversions

An inversion is a pair of indices (i, j) with i < j and p(i) > p(j)

Example:

Input: N = 4, K = 2
Output: 5
Explanation: [
    [1, 3, 4, 2],
    [1, 4, 2, 3],
    [2, 1, 4, 3],
    [2, 3, 1, 4],
    [3, 1, 2, 4],
]