Link Cut Tomato

It is well known that tomatoes form a network by connecting and disconnecting with each other, using their stems like antennas. A connection between two tomatoes can form or break only at the moment the date changes, and the connection state of any two tomatoes does not change more than once a day.

John, a farmer who majored in tomato networks, found a link between the connection states of tomatoes and how ripe they are. According to John's finding, if a ripe tomato and an unripe tomato are connected for a day, the unripe tomato ripens under the influence of the ripe one.

After long research, John built a device that observes the connection states between tomatoes. With this device, you can see which tomatoes are ripe on day $0$ and which tomatoes are connected on day $0$. You can also track when a connection between any two tomatoes forms or breaks.

Chanwoo spent all the money he had for setting problems for the Cheonha Jeil Coding Contest on John's device and $N$ tomatoes numbered $1$ through $N$, but he could not figure out when each tomato ripens. Write a program that computes the ripening day of each tomato from the information obtained from John's device, so that Chanwoo can eat the ripe tomatoes.

The first line contains four integers $N$, $M$, $K$, and $Q$, separated by spaces, which are the number of tomatoes, the number of connected pairs on day $0$, the number of tomatoes that are ripe on day $0$, and the number of changes in connection states. $(1 \leq K \leq N \leq 200\,000;$ $0 \leq M, Q \leq 200\,000)$

The next $M$ lines contain the initial connection states on day $0$, with no duplicates. Each line contains two tomato numbers $a$ and $b$, separated by a space, that are connected on day $0$. $(1 \leq a \lt b \leq N)$

The next line contains the numbers $X_1, X_2, \dotsm, X_K$ of the distinct tomatoes that are ripe on day $0$, separated by spaces. $(1 \leq X_i \leq N)$

The next $Q$ lines describe the changes in connection states in the order they occur. Each line contains a day $T$ and two tomato numbers $x$ and $y$, separated by spaces. If the two tomatoes were connected on day $T-1$, they become disconnected from midnight of day $T$. If they were not connected on day $T-1$, they become newly connected from midnight of day $T$. Every pair $(T, x, y)$ in the input is distinct. $(1 \leq T \leq 200\,000;$ $1 \leq x \lt y \leq N)$

All numbers in the input are integers.

On the first line, print $N$ integers separated by spaces. For the $i$-th tomato, print $-1$ if it never ripens, or the day it ripens otherwise.

The input and output are large, so it is recommended to use the fast I/O described in the language guide on pages 2-4 of the problem set.