The linear fractional transformations are the functions mapping the extended complex plane onto itself.

Given , and , where , and are pairwise distinct complex numbers and , and are also pairwise distinct complex numbers, your task is to calculate for a certain complex number . It can be shown that the answer is always unique to the given contraints.

输入描述:

The input contains several test cases, and the first line contains an integer  , indicating the number of test cases.

To clarify the input format, we denote , , , , ,  and , where  is the imaginary unit that .

Then for each test case, the first line contains four integers , ,  and , the second contains four integers , ,  and , the third line contains four integers , ,  and , and the fourth line contains only two integers  and . It is guaranteed that all these integers are in the range  and the answer  satisfies , where   is the modulus of the complex number .

输出描述:

For each test case, output a line containing two real numbers  and , indicating the real part and the imaginary part of .

Your answer is acceptable if the absolute or relative errors of both the real part and the imaginary part do not exceed . Formally speaking, suppose that your output is  and the jury's answer is , your output is accepted if and only if .

2
-1 0 0 -1
0 1 -1 0
1 0 0 1
0 -1
-1 0 -1 0
0 1 0 -1
1 0 1 0
0 -1

1.000000000000000 0.000000000000000
0.000000000000000 1.000000000000000

In the first sample case we have , and in the second sample case we have .