Sphere#1853

Sphere

3 seconds
256 megabytes
Medium

Place points on the surface of a sphere so that the minimum pairwise distance among these points is as large as possible.

Input

The input contains integers (1 \leq R \leq 1000) and (2 \leq N \leq 4) — the radius of the sphere and the number of points, respectively.

Output

Output a single real number: the largest possible value of the minimum pairwise distance between these points.

Print the first characters of the answer (including the decimal separator), without rounding.

Examples

Example 1

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