1866. Number of Ways to Rearrange Sticks With K Sticks Visible

https://leetcode.com/problems/number-of-ways-to-rearrange-sticks-with-k-sticks-visible

Description

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

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