Blazing New Trails

Your state has just purchased a large, unspoiled tract of land and wants to turn it into a nature park with hiking trails. The land has $n$ places of interest that guests may want to hike to, and $k$ of them are special. The state wants to connect these places with hiking trails.

There are $m$ candidate trails. Each one directly connects two places of interest and has its own cost. The chosen trails must satisfy these constraints:

1. There must be exactly one way to hike from any place to any other place.
2. Exactly $w$ of the chosen trails must directly connect a special place with a regular place.

The state wants to minimize the total cost of blazing the trails. Find that minimum.

The input consists of a single test case.

The first line contains four integers $n$, $m$, $k$ and $w$, where $n$ ($2 \le n \le 2 \times 10^5$) is the number of places, $m$ ($1 \le m \le 5 \times 10^5$) is the number of candidate direct trails between places, $k$ ($1 \le k < n$) is the number of special places, and $w$ ($1 \le w \le n - 1$) is the number of special-regular direct trails the state wants to blaze. The places are numbered $1$ to $n$.

Each of the next $k$ lines contains a single integer $s$ ($1 \le s \le n$), the number of a special place. These values are distinct and given in ascending order.

Each of the next $m$ lines describes a candidate trail with three integers $a$, $b$ and $c$: the trail would connect places $a$ and $b$ ($1 \le a, b \le n$, $a \ne b$) and would cost $c$ ($1 \le c \le 10^5$). No two places have more than one candidate trail between them, and a trail from $a$ to $b$ is the same as a trail from $b$ to $a$.

Print a single integer: the minimum total cost of blazing trails that satisfy the constraints, or $-1$ if it is not possible.