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 $2$.