Two-Step Shortest Path 2

Seojun was delighted to receive a world map from his father as a birthday present. He wants to write a program that finds shortest paths on the world map and give it to his father as a token of thanks. The world map is an undirected graph whose vertices are cities and whose edges are roads between cities, and the length of a road is the weight of the edge. Starting from vertex $X$, find the shortest distance to vertex $Z$ when at least one of the $P$ intermediate vertices must be visited on the way.

The first line gives the number of vertices $N$ ($10 \le N \le 100{,}000$) and the number of edges $M$ ($10 \le M \le 300{,}000$).

The next $M$ lines give edge information u v w, meaning a bidirectional road of integer weight $w$ between city $u$ and city $v$. ($1 \le u, v \le N$, $u \ne v$, $1 \le w \le 1{,}000{,}000$)

The next line gives X Z. ($1 \le X, Z \le N$, $X \ne Z$)

The next line gives $P$. ($1 \le P \le N - 3$)

The next line gives the $P$ distinct intermediate vertices $Y$ ($1 \le Y \le N$, $X \ne Y \ne Z$) separated by spaces.

Print the shortest distance from vertex $X$ to vertex $Z$ when at least one of the $P$ intermediate vertices must be visited on the way. If vertex $Z$ cannot be reached, print -1.