There are `n` uniquely-sized sticks whose lengths are integers from `1` to `n`. You want to arrange the sticks such that exactly `k` sticks are visible from the left. A stick is visible from the left if there are no longer sticks to the left of it.

- For example, if the sticks are arranged `[1,3,2,5,4]`, then the sticks with lengths `1`, `3`, and `5` are visible from the left.

Given `n` and `k`, return the number of such arrangements. Since the answer may be large, return it modulo `109 + 7`.

Example 1:

    Input: n = 3, k = 2
    Output: 3
    Explanation: [1,3,2], [2,3,1], and [2,1,3] are the only arrangements such that exactly 2 sticks are visible.
    The visible sticks are underlined.

Example 2:

    Input: n = 5, k = 5
    Output: 1
    Explanation: [1,2,3,4,5] is the only arrangement such that all 5 sticks are visible.
    The visible sticks are underlined.

Example 3:

    Input: n = 20, k = 11
    Output: 647427950
    Explanation: There are 647427950 (mod 109 + 7) ways to rearrange the sticks such that exactly 11 sticks are visible.

Constraints:

- `1 <= n <= 1000`
- `1 <= k <= n`