Bob has an important meeting tomorrow and he has to reach office on time in morning. His general mode of transport is by car and on a regular day (no car trouble) the probability that he will reach on time is $p_{ot}$. The probability that he might have car trouble is $p_{ct}$. If the car runs into trouble he will have to take a train and only 2 trains out of the available N trains will get him to office on time.

What are the chances that he will reach office on time tomorrow?

Input constraints

$0 \leq p_{ct} \leq 1$

$0 \leq p_{ot} \leq 1$

$N \geq 2$

Input format

First line: $p_{ct}$

Second line: $p_{ot}$

Third line: N

Output format

Probability he will reach in time, rounded to six decimal digits