Six Shooter

Though the original name was "revolving gun", the short-hand "revolver" is universally used. Nearly all early revolvers and many modern ones have six chambers in the cylinder, giving rise to the slang term "six-shooter".

Burton C. Mossman (April 30, 1867-September 5, 1956) was an American lawman and cattleman in the final years of the Old West. He is most remembered for his capture of the notorious border bandit Augustine Chacon in 1902.

Two weeks ago, in Aurora, Illinois where Mossman was born, an old drawing was found. It is believed that the drawing was done by Mossman in his teens. It shows that Mossman was designing a special revolver that allows him to shoot more often than just the usual six times. It is unknown whether Mossman's design was ever implemented. For six and 17 bullets, the cylinder of Mossman's design looks like this.

There is a large circle with radius R and n little circles with radius r that are placed inside on the border of the large circle. Mossman wanted his bullets to be as large as possible, so there should be no space between the circles. We will decide how large the whole revolver will be and how many bullets it shall contain. Your job is, given R and n, to compute r.

Input

The first line contains the number of scenarios. There is at least one scenario and at most 100 scenarios. For each scenario follows a line containing a real number R and an integer n, with 1 <= R <= 100 and 2 <= n <= 100.

Output

The output for every scenario begins with a line containing "Scenario #i:", where i is the number of the scenario starting at 1. Then print the value for r, rounded to three decimal places. Separate the output for the scenarios with a blank line.

Sample Input

4
4.0 6
4.0 17
3.14159 100
42 2

Sample Output

Scenario #1:
1.333

Scenario #2:
0.621

Scenario #3:
0.096

Scenario #4:
21.000