Time Limit: 2 Seconds
Memory Limit: 65536 KB
There is an beautiful ellipse whose curve equation is:
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.