Problem E
Triangle Pendant

Given a point $D$ at height zero and a triangle $\triangle ABC$ with uniform mass, we use three ropes with length $x$, $y$, and $z$ to connect $AD$, $BD$, and $CD$ respectively. The mass of the ropes can be ignored. Let the triangle fall naturally and stabilize at the lowest position of the center of gravity. Find the final heights of points $A$, $B$, and $C$.

Input

There are multiple test cases. The first line of the input contains an integer $T$ (at most $10^4$) indicating the number of test cases. For each test case:

The first and only line contains six integers $x$, $y$, $z$, $a$, $b$ and $c$ ($1 \le x, y, z, a, b, c \le 1000$, $a + b > c$, $a + c > b$, $b + c > a$) indicating the length of three ropes and the length of $BC$, $AC$ and $AB$.

You can assume that the solution always exists.

Output

For each test case output one line containing three real numbers indicating the height of points $A$, $B$ and $C$.

Your answer will be considered correct if the absolute or relative error to the correct answer does not exceed $10^{-4}$.

2
1 1 1 1 1 1
2 3 3 1 1 1

-0.816496580927726 -0.816496580927726 -0.816496580927726
-2.000000000000000 -2.866025403784439 -2.866025403784439