Meeting in the Middle

Junhyung has arranged to meet his friends tomorrow. Junhyung and his friends live in different cities.

The roads connecting the cities are one-way only, so the time to travel from city $A_i$ to city $B_i$ may differ from the time to travel from city $B_i$ to city $A_i$.

Junhyung and his friends want to choose a city $X$ that satisfies the conditions below and meet there.

• The round-trip time is the sum of the time to travel from one's home city to city $X$ and the time to travel from city $X$ back to one's home city.
• They only choose a city that Junhyung and his friends can reach using the roads.
• They choose the city $X$ that minimizes the maximum of the round-trip times of Junhyung and his friends.
• It is guaranteed that there is at least one city that Junhyung and his friends can travel to.

There are many cities, so this is hard to compute. Let us tell Junhyung and his friends the city $X$ on their behalf.

The first line gives the number of cities $N$ and the number of roads $M$.

From the second line to line $M + 1$, the city $A_i$, the city $B_i$, and the time $T_i$ it takes to travel from city $A_i$ to city $B_i$ are given, separated by spaces.

Line $M + 2$ gives the total number of people, Junhyung and his friends, $K$.

Line $M + 3$ gives the numbers $C_i$ of the cities where Junhyung and his friends live, separated by spaces.

Print the number of the city $X$ that satisfies the conditions above. If there are multiple possible cities $X$, print the city numbers in ascending order.

• $3 \le N \le 200$
• $2 \le K \le N$
• $1 \le M \le N \times (N - 1)$
• $1 \le C_i \le N$
• $1 \le T \le 1,000$