{ "data": { "question": { "questionId": "2408", "questionFrontendId": "2327", "categoryTitle": "Algorithms", "boundTopicId": 1632832, "title": "Number of People Aware of a Secret", "titleSlug": "number-of-people-aware-of-a-secret", "content": "

On day 1, one person discovers a secret.

\n\n

You are given an integer delay, which means that each person will share the secret with a new person every day, starting from delay days after discovering the secret. You are also given an integer forget, which means that each person will forget the secret forget days after discovering it. A person cannot share the secret on the same day they forgot it, or on any day afterwards.

\n\n

Given an integer n, return the number of people who know the secret at the end of day n. Since the answer may be very large, return it modulo 109 + 7.

\n\n

 

\n

Example 1:

\n\n
\nInput: n = 6, delay = 2, forget = 4\nOutput: 5\nExplanation:\nDay 1: Suppose the first person is named A. (1 person)\nDay 2: A is the only person who knows the secret. (1 person)\nDay 3: A shares the secret with a new person, B. (2 people)\nDay 4: A shares the secret with a new person, C. (3 people)\nDay 5: A forgets the secret, and B shares the secret with a new person, D. (3 people)\nDay 6: B shares the secret with E, and C shares the secret with F. (5 people)\n
\n\n

Example 2:

\n\n
\nInput: n = 4, delay = 1, forget = 3\nOutput: 6\nExplanation:\nDay 1: The first person is named A. (1 person)\nDay 2: A shares the secret with B. (2 people)\nDay 3: A and B share the secret with 2 new people, C and D. (4 people)\nDay 4: A forgets the secret. B, C, and D share the secret with 3 new people. (6 people)\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "知道秘密的人数", "translatedContent": "

在第 1 天，有一个人发现了一个秘密。

\n\n

给你一个整数 delay ，表示每个人会在发现秘密后的 delay 天之后，每天 给一个新的人 分享 秘密。同时给你一个整数 forget ，表示每个人在发现秘密 forget 天之后会 忘记 这个秘密。一个人 不能 在忘记秘密那一天及之后的日子里分享秘密。

\n\n

给你一个整数 n ，请你返回在第 n 天结束时，知道秘密的人数。由于答案可能会很大，请你将结果对 109 + 7 取余 后返回。

\n\n

 

\n\n

示例 1：

\n\n
输入：n = 6, delay = 2, forget = 4\n输出：5\n解释：\n第 1 天：假设第一个人叫 A 。（一个人知道秘密）\n第 2 天：A 是唯一一个知道秘密的人。（一个人知道秘密）\n第 3 天：A 把秘密分享给 B 。（两个人知道秘密）\n第 4 天：A 把秘密分享给一个新的人 C 。（三个人知道秘密）\n第 5 天：A 忘记了秘密，B 把秘密分享给一个新的人 D 。（三个人知道秘密）\n第 6 天：B 把秘密分享给 E，C 把秘密分享给 F 。（五个人知道秘密）\n
\n\n

示例 2：

\n\n
输入：n = 4, delay = 1, forget = 3\n输出：6\n解释：\n第 1 天：第一个知道秘密的人为 A 。（一个人知道秘密）\n第 2 天：A 把秘密分享给 B 。（两个人知道秘密）\n第 3 天：A 和 B 把秘密分享给 2 个新的人 C 和 D 。（四个人知道秘密）\n第 4 天：A 忘记了秘密，B、C、D 分别分享给 3 个新的人。（六个人知道秘密）\n
\n\n

 

\n\n

提示：

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