A point set is symmetric about a line if and only if there exists satisfying that and are symmetric about the line for all .

Denoting the distance between two points and as . The distance between two non-empty point sets and is . The infimum of a non-empty real number set is the maximum value of which satisfies for all .

lines , , , are given, where two lines may coincide. For a point , define as the intersection of all sets satisfying and is symmetric about for all , , , . There are queries. For each query, given two points and , find the distance between and .

输入描述:

There are multiple test cases. The first line of input contains an integer  (), the number of test cases. For each test case:

The first line contains an integer  and  (, ) -- the number of lines and the number of points.

The -th of the following  lines contains four integers , ,  and  -- the coordinates of  and  such that  passes through  and . It is guaranteed that  or . Two lines may coincide.

The -th of the following  lines contains four integers , ,  and  -- the coordinates of  and .

It is guaranteed that the absolute value of all coordinates in the input does not exceed .

It is guaranteed that the sum of  and the sum of  over all test cases does not exceed .

输出描述:

For each test case:

For each query, output the distance between  and .

The distance you output is correct if the relative error or absolute error to the jury does not exceed .

4
1 1
0 0 1 0
-1 -2 2 1
2 1
0 0 1 0
0 0 0 1
-1 -2 2 1
3 1
0 0 1 0
0 0 0 1
0 0 1 1
-1 -2 2 1
3 1
0 0 1 0
0 0 0 1
0 0 1 2
-1 -2 2 1

3.162277660168
1.414213562373
0.000000000000
0.000000000000

5
1 1
-8 1 -8 10
-7 -5 -4 -6
2 2
-1 -10 -1 -8
10 9 9 10
2 10 -10 5
-4 4 -3 -3
3 1
-5 -10 -5 6
6 10 8 8
7 -2 4 -5
0 -9 -6 -3
3 3
9 8 10 7
1 5 -9 5
4 -2 -3 -9
6 6 -6 -8
2 -7 10 -3
3 -8 8 -9
1 3
10 -9 10 -7
-2 -7 -2 6
-2 9 -9 2
-6 -7 -7 -9

3.162277660168
7.810249675907
7.071067811865
7.211102550928
0.000000000000
0.000000000000
0.000000000000
13.000000000000
9.899494936612
2.236067977500