I want honey!#1292
Misha, like his cartoon friend Winnie the Pooh, loved honey very much. He eagerly awaited the time he could collect honey at the apiary. However, there were several problems, primarily because the bees themselves did not like the day when the bear harvested honey...
Once, during another honey collection, Misha was stung by bees. Not wanting to harm his tireless workers, he simply ran from the apiary, but along the way he overturned one of the cans which was already partially filled with honey. Fortunately for Misha, the can was closed and the honey did not spill...
Curious Marichka became interested in a simple question: what will the level of honey be in the can if it is placed horizontally?
The can consists of cylinders, connected by a truncated cone (see the schematic drawing below, made by Marichka with a branch on sand). Suppose that in the upright position the level of honey in the can is , the height of the lower part of the can is h_b and its diameter is d_b, the height of the upper part is h_n and its diameter is d_n. The total height of the upright can is . You may neglect the thickness of the bottom, walls, and the lid of the can.
The input consists of several test cases. Each test case is on a separate line and contains space-separated real numbers: k\ h_b\ d_b\ h_n\ d_n\ h. A line containing 0\ 0\ 0\ 0\ 0\ 0 marks the end of input and should not be processed.
For each test case, output a single line with the level of honey in the can placed horizontally, to two decimal places.
Example 1