407622: GYM102861 A Sticker Album
Description
The Sticker Album of the ICPC 2020 Nlogonian Subregional just came out! Competitive programming hooligans all over the country are buying albums and collecting stickers, to celebrate the competition.
This sticker album is special because all stickers are equal: a picture of this year's trophy. To complete the album, you just need to collect enough stickers to fill all the slots in it.
You may be asking yourself: where is the fun in collecting those stickers? Well, to make things interesting, the stickers are sold in packets, each with a random number of stickers! Fans celebrate when they find a high number of stickers in a packet, make fun of those who got unlucky and found low numbers of stickers, and brag about filling their whole albums with just a few packets.
You just acquired your own album, and want to start filling it! But before buying your first sticker packets, you wondered: on average, how many packets does one need to buy in order to fill an album?
InputThe only input line contains three integers $$$N$$$, $$$A$$$ and $$$B$$$, separated by a single space, satisfying $$$1 \le N \le 10^6$$$, $$$0 \le A \le B \le 10^6$$$ and $$$B > 0$$$, where:
- $$$N$$$ is the number of stickers it takes to fill an album;
- $$$A$$$ is the minimum number of stickers in a packet;
- $$$B$$$ is the maximum number of stickers in a packet.
The output consists of a single line, which must contain the expected number of packets it takes to complete an album. The number will be considered correct if it is within an absolute or relative error of $$$10^{-5}$$$ of the correct answer.
ExamplesInput40 0 2Output
40.33333Input
100 1 10Output
18.72727Input
30 3 3Output
10.00000Input
314 5 8Output
48.74556