# 1621. Number of Sets of K Non-Overlapping Line Segments

https://leetcode.com/problems/number-of-sets-of-k-non-overlapping-line-segments

## Description

Given `n` points on a 1-D plane, where the `ith` point (from `0` to `n-1`) is at `x = i`, find the number of ways we can draw **exactly** `k` **non-overlapping** line segments such that each segment covers two or more points. The endpoints of each segment must have **integral coordinates**. The `k` line segments **do not** have to cover all `n` points, and they are **allowed** to share endpoints.

Return _the number of ways we can draw_ `k` _non-overlapping line segments_\*.\* Since this number can be huge, return it **modulo** `109 + 7`.

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/09/07/ex1.png)

```
**Input:** n = 4, k = 2
**Output:** 5
**Explanation:**The two line segments are shown in red and blue.
The image above shows the 5 different ways {(0,2),(2,3)}, {(0,1),(1,3)}, {(0,1),(2,3)}, {(1,2),(2,3)}, {(0,1),(1,2)}.
```

**Example 2:**

```
**Input:** n = 3, k = 1
**Output:** 3
**Explanation:** The 3 ways are {(0,1)}, {(0,2)}, {(1,2)}.
```

**Example 3:**

```
**Input:** n = 30, k = 7
**Output:** 796297179
**Explanation:** The total number of possible ways to draw 7 line segments is 3796297200. Taking this number modulo 109 + 7 gives us 796297179.
```

**Example 4:**

```
**Input:** n = 5, k = 3
**Output:** 7
```

**Example 5:**

```
**Input:** n = 3, k = 2
**Output:** 1
```

**Constraints:**

* `2 <= n <= 1000`
* `1 <= k <= n-1`

## ac

```java
```
