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

Medium

Given n points on a 1-D plane, where the <code>i^th</code> 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 <code>10⁹ + 7</code>.

Example 1:

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.

Constraints:

• 2 <= n <= 1000

• 1 <= k <= n-1