Number of People Aware of a Secret
On day 1 , one person discovers a secret.
You receive 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 , produce 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 .
Input: n = 6, delay = 2, forget = 4
Output: 5
Explanation:
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Day 1: Suppose the first person is named A. (1 person)
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Day 2: A is the only person who knows the secret. (1 person)
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Day 3: A shares the secret with a new person, B. (2 people)
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Day 4: A shares the secret with a new person, C. (3 people)
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Day 5: A forgets the secret, and B shares the secret with a new person, D. (3 people)
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Day 6: B shares the secret with E, and C shares the secret with F. (5 people)
Input: n = 4, delay = 1, forget = 3
Output: 6
Explanation:
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Day 1: The first person is named A. (1 person)
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Day 2: A shares the secret with B. (2 people)
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Day 3: A and B share the secret with 2 new people, C and D. (4 people)
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Day 4: A forgets the secret. B, C, and D share the secret with 3 new people. (6 people)
Constraints
2 <= n <= 10001 <= delay < forget <= n
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