2327. Number of People Aware of a Secret

Medium

684

105

On day `1`

, one person discovers a secret.

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.

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** `10`

.^{9} + 7

**Example 1:**

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

**Example 2:**

Input:n = 4, delay = 1, forget = 3Output:6Explanation:Day 1: The first person is named A. (1 person) Day 2: A shares the secret with B. (2 people) Day 3: A and B share the secret with 2 new people, C and D. (4 people) Day 4: A forgets the secret. B, C, and D share the secret with 3 new people. (6 people)

**Constraints:**

`2 <= n <= 1000`

`1 <= delay < forget <= n`

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