Description

Input

The first line contains three integers $n$, $m$ and $k$ ($2 \leq k \leq n \leq 10^5$, $n-1 \leq m \leq 10^5$) — the number of vertices, the number of edges and the number of special vertices.

The second line contains $k$ distinct integers $x_1, x_2, \ldots, x_k$ ($1 \leq x_i \leq n$).

Each of the following $m$ lines contains three integers $u$, $v$ and $w$ ($1 \leq u,v \leq n, 1 \leq w \leq 10^9$), denoting there is an edge between $u$ and $v$ of weight $w$. The given graph is undirected, so an edge $(u, v)$ can be used in the both directions.

The graph may have multiple edges and self-loops.

It is guaranteed, that the graph is connected.

Output

The first and only line should contain $k$ integers. The $i$-th integer is the distance between $x_i$ and the farthest special vertex from it.

2 3 2
2 1
1 2 3
1 2 2
2 2 1

2 2 

4 5 3
1 2 3
1 2 5
4 2 1
2 3 2
1 4 4
1 3 3

3 3 3 

Note

In the first example, the distance between vertex $1$ and $2$ equals to $2$ because one can walk through the edge of weight $2$ connecting them. So the distance to the farthest node for both $1$ and $2$ equals to $2$.

In the second example, one can find that distance between $1$ and $2$, distance between $1$ and $3$ are both $3$ and the distance between $2$ and $3$ is $2$.

The graph may have multiple edges between and self-loops, as in the first example.