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ZOJ Problem Set - 3919

Time Limit: 1 Second      Memory Limit: 65536 KB      Special Judge

There is an beautiful ellipse whose curve equation is:

\frac {x^2}{a^2} + \frac {y^2}{b^2} = 1 (a > b > 0)

There is a parallelogram named P inscribed in this ellipse. At the same time, the parallelogram P is externally tangent to some circle center at the origin (0,0).

Now your task is to output the maximum and minimum area of P among all possible conditions.


The input consists of multiple test cases.

For each test case, there is exactly one line consists of two integers a and b. 0 < b <= a <= 109


For each test case, output one line of two one-space splited numbers: the maximum area and the minimum area. The absolute or relative error of the coordinates should be no more than 10-6.

Sample Input

1 1

Sample Output

2 2

Author: ZHANG, Ruixiang
Source: ZOJ Monthly, February 2016
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