Rectangle Folding

In the following figure you can see a rectangular card that has width W and length L. Assume the thickness of the card is zero. Four x by x squares are cut from the four corners of the card shown by the black dotted lines. Then the card is folded along the magenta lines to make a box without a cover.

Given the width and height of the box, you need to find the value of x for which the box has maximum and minimum volume.


The input file contains several lines of input. Each line contains two positive floating-point numbers L (0.0 < L < 10000.0) and W (0.0 < W < 10000.0); which indicate the length and width of the card respectively.

Output: box.out

For each line of input you should print one line of output, which contains two floating-point numbers, separated by a single space. The floating-point numbers should contain three digits after the decimal point. The first floating point number indicates the value for which the volume of the box is maximal. The second floating point indicates the largest value for which the volume of the box is minimal.

Sample Input

1 1
2 2
3.0 3.0

Sample Output

0.167 0.500
0.333 1.000
0.500 1.500