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ZOJ Problem Set - 2092
Fastest Drop

Time Limit: 2 Seconds      Memory Limit: 65536 KB

There is a sphere on the groud, and it's center is (0,0,0). A dot P is out of the sphere.

Please find a dot Q on the sphere, then join P and Q with a direct path to make a small ball drop from P to Q the fastest.

(There will be no friction at all. )


Input consists of several test cases. Each case will contain 4 positive integer x, y, z and R.

x, y, z mean the position of the dot P. R is the radius of the sphere. (z > 0, R > 0)

The input ends with 0 0 0 0.


Output like this: The ball need xxx seconds slide to the dot (x1, y1, z1).

x1, y1, z1 mean the dot Q. And xxx means the drop time.

Accurate to 4 decimal places.

Sample Input

10 10 10 5
0 0 0 0

Sample Output

The ball need 1.9343 seconds slide to the dot (3.5294,3.5294,0.2941)

Author: YU, Xing
Source: ZOJ Monthly, March 2004
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