###### Category

###### Similar Problems

## 0740. Ball in a Dream

###### Time limit : 1000 ms

Memory limit : 64 mb

A little boy likes throwing balls in his dreams. He
stands on the endless horizontal plane and throws a ball at an angle of *a* degrees to the plane. The starting
speed of the ball is *V* m/s. The ball flies some distance,
falls down, then jumps off, flies again, falls again, and so on.

As far as everything may happen in a dream, the laws of the ball's motion differ from the usual laws of physics:

- the ball moves in the
gravity field with acceleration of gravity equal to 10 m/s
^{2}; - the rebound angle equals the angle of fall;
- after every fall, the
kinetic energy of the ball decreases by a factor of
*K*; - there is no air in the dream;
- "Pi" equals to 3.1415926535.

Your task is to determine the maximal distance from the point of throwing that the ball can fly

**Input**

The input contains three numbers: 0
≤ *V* ≤ 5000, 0 ≤ *a* ≤ 90, and *K* > 1 separated by spaces. The
numbers *V* and *a* are
integers; the number *K* is real.

**Output**

The output should contain the required distance in meters rounded to two fractional digits.

Samples

№ |
Input |
Output |

1 |
5 15 2.50 |
2.08 |

Text from: acm.timus.ru