408511: GYM103176 D Drawing Circles

David is a little boy who loves drawing circles on the wall. He is now planning on a $$$N$$$-day project. Before the start of the project, he draws two big circles on the wall, so that they touch each other, and both touch the ground. The one on the left has radius $$$r_1$$$ units, and the one on the right has radius $$$r_2$$$ units.

Then, on each day of the project, David will draw one more circle on the wall, while this circle must fulfill the following requirements:

• It is a circle that does not overlap with any other circles drawn before
• It must touch exactly two other circles drawn before
• It must touch the ground
• Among all possible ways of drawing the new circle according to the rules above, David will draw the one with the largest radius. If they are still more than one possibility, he will draw the leftmost one.

Can you predict the radius of the circle that will be drawn on each of the $$$N$$$ days?

The only line contains three integers, $$$r_1$$$, $$$r_2$$$ and $$$N$$$ ($$$1\le r_1, r_2, N\le 3\times 10^5$$$).

Output $$$N$$$ numbers, the $$$i$$$-th number denotes the radius of the circle that David will draw on the $$$i$$$-th day.

Your answer will be accepted if for each and every radius, the relative error or absolute error, whichever is less, is not greater than $$$10^{-6}$$$.

9 4 4

1.44 0.734694 0.5625 0.444444

10 10 1

2.5000000000 

In Sample 1, after $$$N=4$$$ days, a part of the wall will look like: