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 = 10
    Output: 1.00000
    Explanation: Alice gets a single card, then stops.

Example 2:

    Input: n = 6, k = 1, maxPts = 10
    Output: 0.60000
    Explanation: Alice gets a single card, then stops.
    In 6 out of 10 possibilities, she is at or below 6 points.

Example 3:

    Input: n = 21, k = 17, maxPts = 10
    Output: 0.73278

Constraints:

- `0 <= k <= n <= 104`
- `1 <= maxPts <= 104`