{ "data": { "question": { "questionId": "1996", "questionFrontendId": "1866", "boundTopicId": null, "title": "Number of Ways to Rearrange Sticks With K Sticks Visible", "titleSlug": "number-of-ways-to-rearrange-sticks-with-k-sticks-visible", "content": "

There are n uniquely-sized sticks whose lengths are integers from 1 to n. You want to arrange the sticks such that exactly k sticks are visible from the left. A stick is visible from the left if there are no longer sticks to the left of it.

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Given n and k, return the number of such arrangements. Since the answer may be large, return it modulo 109 + 7.

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Example 1:

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\nInput: n = 3, k = 2\nOutput: 3\nExplanation: [1,3,2], [2,3,1], and [2,1,3] are the only arrangements such that exactly 2 sticks are visible.\nThe visible sticks are underlined.\n
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Example 2:

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\nInput: n = 5, k = 5\nOutput: 1\nExplanation: [1,2,3,4,5] is the only arrangement such that all 5 sticks are visible.\nThe visible sticks are underlined.\n
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Example 3:

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\nInput: n = 20, k = 11\nOutput: 647427950\nExplanation: There are 647427950 (mod 109 + 7) ways to rearrange the sticks such that exactly 11 sticks are visible.\n
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Constraints:

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