G. Grandmapocalipse
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Oh no! Your cookie business has grown too successful, and you have mistreated the grandmas so much that you have awakened their fury, triggering the Grandmapocalypse. The only way to stop them is to travel to the milk sea of the chocolate islands, and make a ritual to the golden cookie.

The ritual consists of choosing 3 chocolate islands such that the golden cookie is inside the triangle they form when seen from above (it has to be completely inside, so it won't work if the cookie is collinear with two of the islands).

Sadly, due to indiscriminating chocolate mining from your side, the cookie islands have grown smaller and most of them are under the milk sea. But there's still hope! You know the location of each island (given by $$$x$$$ and $$$y$$$ coordinates), its height (given by $$$z$$$), and know that the Grandmatriarch is drinking the milk sea such that its height will go down in a uniform way of 1 meter per hour. Currently, the milk sea is $$$h$$$ meters tall, and you want to know exactly how many hours will pass before you can do the ritual. A cookie is available for you to pick if its height is greater than or equal to the milk sea height.

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

Input

On the first line, an integer $$$N$$$ $$$(1\leq N \leq 10^5)$$$ and a real number $$$h$$$ $$$(1\leq h \leq 10^9)$$$, the number of chocolate islands and the height of the sea at the start, respectively.

On the next $$$N$$$ lines, 3 real numbers $$$x_i,y_i,z_i$$$ ($$$-10^9\leq x_i,y_i,z_i\leq 10^9$$$), indicating the coordinates of the $$$i$$$-th island.

On the last line 2 real numbers, $$$a$$$ and $$$b$$$ ($$$-10^9\leq a, b\leq 10^9$$$), the coordinates of the golden cookie.

All coordinates will be given with two digits after the decimal point. It is guaranteed that if two islands have the same $$$x$$$ and $$$y$$$ coordinates, then their height ($$$z$$$) it's different.

Output

A real number, indicating how many hours will have to pass before you can do the ritual. If you won't be able to defeat the grandmapocalypse, print "-1".

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

Examples
Input
4 10.00
1.00 1.00 7.00
3.00 1.00 11.00
3.00 3.00 -2.00
1.00 3.00 15.00
2.50 2.50
Output
12.0000000000
Input
3 10.00
1.00 1.00 20.00
3.00 1.00 6.47
2.00 3.00 2.45
5.00 3.00
Output
-1
Note

"A local news station runs a 10-minute segment about your cookies. Success!"

This statement has been modified to include the clarifications made during the competition.