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.
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Example 1:
\n![\"\"](\"https://assets.leetcode.com/uploads/2020/09/07/ex1.png\")
\n\nInput: n = 4, k = 2\nOutput: 5\nExplanation: The two line segments are shown in red and blue.\nThe 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)}.\n\n\nExample 2:
\n\n\nInput: n = 3, k = 1\nOutput: 3\nExplanation: The 3 ways are {(0,1)}, {(0,2)}, {(1,2)}.\n\n\nExample 3:
\n\n\nInput: n = 30, k = 7\nOutput: 796297179\nExplanation: The total number of possible ways to draw 7 line segments is 3796297200. Taking this number modulo 109 + 7 gives us 796297179.\n\n\n
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Constraints:
\n\n2 <= n <= 10001 <= k <= n-1Compiled with clang 11 using the latest C++ 20 standard.
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