Number of Ways to Rearrange Sticks With K Sticks Visible
There are n uniquely-sized sticks whose lengths are integers from 1 to n.
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.
Given n and k, return the number of such arrangements. Since the answer may be large, return it modulo 10^9 + 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 10^9 + 7) ways to rearrange the sticks such that exactly 11 sticks are visible.
Constraints
- 1 <= n <= 1000
- 1 <= k <= n
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