Alternative Mart

Minsik lives alone in OJUZ City. OJUZ City has $N$ regions and $M$ bidirectional roads, and $K$ of the $N$ regions have a discount mart. Region numbers are integers from 1 to $N$. At most one road directly connects any two regions, and the two endpoints of every road are different. Any region can reach any other region.

When his work ends, Minsik goes to a discount mart to buy cooking ingredients and snacks, then returns to his apartment. He always takes the fastest route to a discount mart. Sometimes some marts are closed. When a mart is closed, the route he used before may no longer work.

Write a program that finds, for each query, which discount mart Minsik should go to. Ignore the time needed to travel from the mart back home.

The first line contains $N$, $M$, $K$, and $Q$, the number of regions, roads, discount marts, and queries. ($2 \le N \le 50\,000$, $N-1 \le M \le 80\,000$, $1 \le K \le N$, $1 \le Q \le 50\,000$)

The second line contains the $K$ region numbers with discount marts, in ascending order.

Each of the next $M$ lines contains two endpoints $P_i$, $Q_i$ and the length $V_i$ of a road. ($1 \le P_i, Q_i \le N$, $1 \le V_i \le 10\,000$)

Each of the next $Q$ lines is a query: a start region $S$, the number of closed marts $X$, and the region numbers $C_1, \ldots, C_X$ of the closed marts. ($0 \le X \le \min(10, K-1)$, $1 \le S, C_i \le N$)

For each query, print the number of the discount mart Minsik should visit (the region where it is located) and the minimum time to get there. If several marts tie for the shortest time, print the smallest number.