{ "data": { "question": { "questionId": "1725", "questionFrontendId": "1621", "boundTopicId": null, "title": "Number of Sets of K Non-Overlapping Line Segments", "titleSlug": "number-of-sets-of-k-non-overlapping-line-segments", "content": "

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.

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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:

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\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
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Example 2:

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\nInput: n = 3, k = 1\nOutput: 3\nExplanation: The 3 ways are {(0,1)}, {(0,2)}, {(1,2)}.\n
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Example 3:

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\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
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Constraints:

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