0230. The Greatest Angle

Имя входного файла: angle.in
Имя выходного файла: angle.out
Ограничение по времени: 250 ms
Ограничение по памяти: 64 megabytes

Consider two points A and B located strictly inside of some circle in Cartesian coordinate system. You task is to find a point C on the circle such that the angle ACB is maximal possible.

Input file

On first line of input file there is one integer N – number of tests (1 ≤ N ≤ 10000). I+1-th line describes I-th test case in format X0, Y0, R, XA, YA, XB, YB, where (X0, Y0) is center of the circle, R is radius of the circle, (XA, YA) are point A coordinates, (XB, YB) are point B coordinates. All numbers are integers. X0, Y0, R are not greater than 10000 by absolute value.

Output file

Output file must contain N lines, exactly one for each test case. For each case you must output XC and YC – coordinates of point C, described in statement, with precision of six digits after decimal point. If there are many solutions, output any one of them.

Example:

angle.inangle.out
2 0 0 2 1 1 -1 1 0 0 2 0 1 1 0 0.000000 2.000000 1.414214 1.414214


Источник: Petrozavodsk Winter 2004. SPb ETU Contest, Sunday, February 01

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