Number of Ways to Rearrange Sticks With K

lcpy gen -n 1866   # by problem number
lcpy gen -s rearrange_sticks   # by problem name

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.

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.

Input: n = 20, k = 11
Output: 647427950
Explanation: There are 647427950 (mod 10^9 + 7) ways to rearrange the sticks such that exactly 11 sticks are visible.

class Solution:
    # Time: O(n * k)
    # Space: O(k)
    def rearrange_sticks(self, n: int, k: int) -> int:
        mod = 1_000_000_007
        prev = [0] * (k + 1)
        prev[0] = 1
        for i in range(1, n + 1):
            curr = [0] * (k + 1)
            hi = min(i, k)
            for j in range(1, hi + 1):
                curr[j] = ((i - 1) * prev[j] + prev[j - 1]) % mod
            prev = curr
        return prev[k]