Number of Sets of K Non-Overlapping Line Segments
Given n points on a 1-D plane, where the i^th point from 0 to n - 1 is at x = i, find the number of ways to 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 to draw k non-overlapping line segments. Since this number can be huge, return it modulo 10^9 + 7.
Example 1
Input
n = 4, k = 2Output
5The 5 ways are {(0,2),(2,3)}, {(0,1),(1,3)}, {(0,1),(2,3)}, {(1,2),(2,3)}, and {(0,1),(1,2)}.
Example 2
Input
n = 3, k = 1Output
3The 3 ways are {(0,1)}, {(0,2)}, and {(1,2)}.
Constraints
- 2 <= n <= 1000
- 1 <= k <= n-1