Having developed a COVID-19 vaccine, CodeVax gives you one final assignment: Deliver the CodeVax vaccine to cities around the world.

More specifically, the planet Earth has a radius of ~R~ and a centre at ~(0,0,0)~. There are ~N~ cities numbered from ~1~ to ~N~ on Earth's surface. Additionally, there are ~M~ bidirectional roads connecting cities together. The distance between two cities a b is defined as the shortest distance between the two points by travelling on the surface of planet Earth. Each city has ~v_i~ active COVID-19 cases. Furthermore, of the ~N~ cities, only ~K~ of them have airports. You start in city ~1~ and can travel along roads at ~1~ unit per second.

Wanting to help the most people, you decide you will deliver the CodeVax vaccines to the city with the highest number of active COVID-19 cases you can reach, while still getting to an airport strictly before ~T~ seconds. Output the number of active COVID-19 cases of such a city or -1 if you can't reach an airport under ~T~ seconds.

Input Specification

The first line of input will contain the positive integers ~N~, ~M~, ~R~, ~T~, and ~K~.

The next line will contain ~K~ integers, denoting which of the ~N~ cities contain an airport to take you home.

The next ~N~ lines will contain the integer ~v_i~ and the numbers ~x_i~, ~y_i~, ~z_i~, the number of active COVID-19 cases and the coordinates of the ~i~th city. The coordinates of each city will be rounded up to ten decimal places.

The next ~M~ lines will contain two integers ~a~ and ~b~, meaning there is a bidirectional road between cities ~a~ and ~b~.

Output Specification

Output the number of active COVID-19 cases of the most infected city you can reach while reaching a city that has an airport. If you are unable to reach any airport strictly before ~T~ seconds, print -1.

Constraints

~1 \le N \le 10^5~

~1 \le M, R \le 10^6~

~0 \le T, v_i \le 10^9~

~1 \le K, K_i \le N~

~1 \le a, b \le N~

You may visit any road and/or city multiple times. All ~K_i~ are distinct. Not all roads are guaranteed to be distinct. It is guaranteed that the cities will lie on the Earth's surface to within an absolute error of less than ~10^{-3}~.

Sample Input 1

3 3 3 7 2
2 3
0 -2.5000000000 0.0000000000 1.6583123952
1 1.5000000000 2.0000000000 1.6583123952
2 0.0000000000 0.0000000000 -3.0000000000
1 2
2 3
1 3

Sample Output 1

2

Explanation for Sample 1

You can travel directly to city ~3~ and deliver the vaccines there in under ~7~ seconds. From there, you can leave through the airport at city ~3~.

Sample Input 2

3 3 3 6 2
2 3
0 -2.5000000000 0.0000000000 1.6583123952
1 1.5000000000 2.0000000000 1.6583123952
2 0.0000000000 0.0000000000 -3.0000000000
1 2
2 3
1 3

Sample Output 2

1

Explanation for Sample 2

You cannot travel to city ~3~ in under ~6~ seconds. Therefore you must head to city ~2~, deliver the vaccines there, and leave through the airport at city ~2~.