Count permutations with exactly n inversions

You are given two integers **m** and **n**. Consider all permutations of the array `[1, 2, ..., m]` (each number from 1 to m appears exactly once). A permutation `perm` (0-indexed) has an **inversion** pair `(x, y)` if: - `0 <= x < y < m`, and - `perm[x] > perm[y]` A permutation is called **special** if it contains **exactly `n` inversions**. Return the **number of special permutations** modulo **10^9 + 7**. #### Examples 1) **Input:** `m = 3, n = 0` **Output:** `1` **Explanation:** Only `[1, 2, 3]` has 0 inversions. 2) **Input:** `m = 3, n = 1` **Output:** `2` **Explanation:** `[1, 3, 2]` and `[2, 1, 3]` each have exactly 1 inversion. #### Constraints - `1 <= m <= 1000` - `0 <= n <= 1000`