Yeehaa!

George wants to become a western hero, so he dreams of a special revolver that can fire more than the usual six shots. The cylinder that holds the bullets looks like the figure below (examples for 6 and 17 bullets):

Figure 1: Examples

There is one large circle of radius $R$, and $n$ small circles of radius $r$ placed inside it along its border. To make the bullets as large as possible, the small circles are packed with no gaps: each small circle is tangent to the large circle and also to its two neighboring small circles. Given $R$ and $n$, compute $r$.

The first line contains the number of scenarios. Each of the following lines describes one scenario and contains a real number $R$ and an integer $n$, with $1 \le R \le 100$ and $2 \le n \le 100$.

For each scenario, first print a line Scenario #i:, where $i$ is the scenario number starting at 1. On the next line, print the value of $r$ rounded to three decimal places. Separate consecutive scenarios with a blank line.