2013. Ball in dream

单点时限: 2.0 sec

内存限制: 256 MB

A little boy likes throwing balls in his dreams. He stays on the endless horizontal plane and throws a ball at the angle a degrees with the starting speed, which is equal to 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 dream the laws of ball’s motion differ from usual physics laws:

  • The ball flies with acceleration of gravity equal to 10 m/s2;

  • Angle of jumping off equals to angle of falling down;

  • After every falling down the kinetic energy of the ball decreases in K times;

  • There is no air in dream;

  • “Pi” equals to 3.1415926535.

Your task is to determine the maximum distance the ball can fly.

输入格式

There are several test cases.Each input contains three numbers: 0 ≤ V ≤ 100, 0 ≤ a ≤ 90 and K > 1, separated by the spaces. Numbers V and a are integers, K is real.

输出格式

Output should contain the only number ― desired distance rounded to two digits after decimal point.

样例

Input
5 15 2.50
Output
2.08

34 人解决,41 人已尝试。

49 份提交通过,共有 117 份提交。

3.9 EMB 奖励。

创建: 14 年,1 月前.

修改: 4 年,5 月前.

最后提交: 11 月,1 周前.

来源: Fifth High School Children Programming Contest, Ekaterinburg

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