思考题 for Hakurei Reimu

# Legacy of Lunatic Kingdom

ZJS loves playing Touhou. In the famous STG game *Touhou:Legacy of Lunatic Kingdom* the game rules are defined as follows:

The game consists of N "stages". Player start from Stage 1 and ends at Stage N. In i-th stage, our little ZJS has a probability

But, ZJS has some BOMBs. He can use BOMB in some stages.The probability of the stage i to pass after using a bomb is

Note that, after retrying a stage with a bomb, the probability of passing that stage is still

Assume that beating each stage once needs 1 unit of time. For each bomb placement, you need to calculate the expected time to pass all stages. Then you need to print the minimum one among all these data. If the minimum one is INF, print -1 instead.

YP is calling him so he asked the Orange Boy to help.

# Constriants

Subtask 1(30%):N=6,B=3

Subtask 2(30%):N,B<=20

Subtask 3(10%):N,B<=100

Subtask 4(10%):N,B<=1000

Subtask 5(10%):N,B<=1e5

Subtask 6(5%):N<=1e5,B=0

Subtask 7(5%):N<=1e5,B=1

For all subtask, 0<=B<=N<=1e5 holds.