Two Tables

Description:

Input:

The first line contains the single integer $$$t$$$ ($$$1 \le t \le 5000$$$) — the number of the test cases.

The first line of each test case contains two integers $$$W$$$ and $$$H$$$ ($$$1 \le W, H \le 10^8$$$) — the width and the height of the room.

The second line contains four integers $$$x_1$$$, $$$y_1$$$, $$$x_2$$$ and $$$y_2$$$ ($$$0 \le x_1 < x_2 \le W$$$; $$$0 \le y_1 < y_2 \le H$$$) — the coordinates of the corners of the first table.

The third line contains two integers $$$w$$$ and $$$h$$$ ($$$1 \le w \le W$$$; $$$1 \le h \le H$$$) — the width and the height of the second table.

Output:

For each test case, print the minimum distance you should move the first table, or $$$-1$$$ if there is no way to free enough space for the second table.

Your answer will be considered correct if its absolute or relative error doesn't exceed $$$10^{-6}$$$.

Sample Input:

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

Sample Output:

1.000000000
-1
2.000000000
2.000000000
0.000000000

Note:

The configuration of the first test case is shown in the picture. But the movement of the first table is not optimal. One of the optimal movement, for example, is to move the table by $$$(0, -1)$$$, so the lower left corner will move from $$$(2, 1)$$$ to $$$(2, 0)$$$. Then you can place the second table at $$$(0, 3)-(4, 5)$$$.

In the second test case, there is no way to fit both tables in the room without intersecting.

In the third test case, you can move the first table by $$$(0, 2)$$$, so the lower left corner will move from $$$(0, 3)$$$ to $$$(0, 5)$$$.