Given an array containing the radii of circular cakes and the number of guests, determine the largest piece that can be cut from the cakes such that every guest gets a piece of the cake with the same area. It is not possible that a single piece has some part of one cake and some part of another cake and each guest is served only one piece of cake.

Example 1.

Radii = [ 1, 1, 1, 2, 2, 3] numberOfGuests = 6.

Output: 7.0686

Reason being you can take the area of the cake with a radius of 3, and divide by 4. (Area 28.743 / 4 = 7.0686)

Use a similary sized piece from the remaining cakes of radius 2 because total area of cakes with radius 2 are > 7.0686

Example 2.

Radii [4, 3, 3] numberOfGuests = 3

Output: 28.2743

Example 3.

Radi [6, 7] numberOfGuests = 12

Output: 21.9911