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

Count the number of ways to choose exactly k non-overlapping line segments on n collinear integer points (points 0..n-1), where each segment covers at least two points, segments may share endpoints, and the answer is modulo 1e9+7. This is typically solved with dynamic programming / combinatorics over positions and segments (n ≤ 1000, k ≤ n−1).