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 lengths1,3, and5are 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 <= 10001 <= k <= n