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ZOJ Problem Set - 2517
Painting Ellipses

Time Limit: 2 Seconds      Memory Limit: 65536 KB

An ellipse can be determined by a pair of a and b, the half lengths of its horizontal and vertical axes, respectively (as shown in Figure 1). CYJJ loves ellipses so much that she plans to paint the walls of her room with all kinds of crossed ellipses. The two ellipses share the same center and axes as shown in Figure 2.

She has to be so accurate that with any amount of paint, she wants the design to exactly use up the paint. Well, it is a good exercise to her students. So you are assigned to do this homework now.

The input consists of several test cases, each occupies a line with 4 positive numbers: S, a1, b1, and a2, where S is the total area that should be painted, ai's are the half lengths of the horizontal axes of the two ellipses, and b1 is the half length of the vertical axis of the first ellipse.

For each test case, output in a line the half length of the vertical axis of the second ellipse, accurate up to 2 decimal places. If it is impposible to paint a cross, print "Impossible" instead.

Sample Input:
221.43 10 5 5
314 10 10 11
Sample Output:

Author: CHEN, Yue
Source: CYJJ's Funny Contest #2, Relaxing on Math
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