#D7322. Star
Star
Star
Problem
Find the area of a regular N / K polygon inscribed in a circle with a radius of 1.
However, a regular N / K polygon is defined as "the outermost figure that takes N points on the circumference at equal intervals and connects each point every K-1".
For example, a 5/2 polygon can be drawn as follows. First, take five points at equal intervals on the circumference of radius 1.
Sample Input 2 diagram
Next, connect each point every other 2-1 = 1.
Sample Input 2 diagram
The outermost figure is a regular 5/2 square.
Sample Input 2 diagram
Constraints
The input satisfies the following constraints.
- 5 ≤ N ≤ 106
- 1 <K <N / 2
- N and K are integers that are relatively prime
Input
The input is given in the following format.
N K
Two integers N and K are given on one line.
Output
Output the area of a regular N / K polygon inscribed in a circle with a radius of 1 on one line. An error of 10-5 or less is acceptable.
Examples
Input
5 2
Output
1.12256994
Input
20 3
Output
2.93114293
Input
7 3
Output
1.08395920
Input
100000 3
Output
3.14159265
inputFormat
Input 2 diagram
Next, connect each point every other 2-1 = 1.
Sample Input 2 diagram
The outermost figure is a regular 5/2 square.
Sample Input 2 diagram
Constraints
The input satisfies the following constraints.
- 5 ≤ N ≤ 106
- 1 <K <N / 2
- N and K are integers that are relatively prime
Input
The input is given in the following format.
N K
Two integers N and K are given on one line.
outputFormat
Output
Output the area of a regular N / K polygon inscribed in a circle with a radius of 1 on one line. An error of 10-5 or less is acceptable.
Examples
Input
5 2
Output
1.12256994
Input
20 3
Output
2.93114293
Input
7 3
Output
1.08395920
Input
100000 3
Output
3.14159265
样例
100000 33.14159265