n uniquely-sized sticks whose lengths are integers from
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.
[1,3,2,5,4], then the sticks with lengths
5are visible from the left.
k, return the number of such arrangements. Since the answer may be large, return it modulo
109 + 7.
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 109 + 7) ways to rearrange the sticks such that exactly 11 sticks are visible.
1 <= n <= 1000
1 <= k <= n