Sphere

Want to place on the surface of a sphere of N points so that the minimum of the pairwise distances between these points was the maximum possible.

Input

In a single line of input contains integers R (1 ≤ R ≤ 1000) and N (2 ≤ N ≤ 4) — the sphere radius and the number of points, respectively.

Output

The output file output single real number - the maximum possible value of the minimum of pairwise distances between these points.

This conclusion follows the first 10000 characters response (including a separator whole and fractional parts), without rounding.

Examples