Given two integers n and k, return the number of distinct arrays consisting of integers from $1$ to n that contain exactly k inverse pairs. Since the answer can be very large, return it modulo $10^9 + 7$.

An inverse pair in an array nums is defined as a pair of indices $(i, j)$ such that $0 \leq i < j <$ nums.length and nums[i] $>$ nums[j].

Constraints:

• $1 \leq$ n $\leq 1000$

• $0 \leq$ k $\leq 1000$

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