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# 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`

## ac

```java
```