New 21 Game
Alice plays the following game, loosely based on the card game "21".
Alice starts with 0 points and draws numbers while she has less than k points. During each draw, she gains an integer number of points randomly from the range [1, maxPts], where maxPts is an integer. Each draw is independent and the outcomes have equal probabilities.
Alice stops drawing numbers when she gets k or more points.
Return the probability that Alice has n or fewer points.
Answers within 10^-5 of the actual answer are considered accepted.
Example 1
Input
n = 10, k = 1, maxPts = 10Output
1Alice gets a single card, then stops.
Example 2
Input
n = 6, k = 1, maxPts = 10Output
0.6Alice gets a single card, then stops; in 6 out of 10 possibilities, she is at or below 6 points.
Constraints
- 0 <= k <= n <= 10^4
- 1 <= maxPts <= 10^4
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