Connect the Forest

You are given a forest with $N$ vertices and $M$ edges. The vertices are numbered $0$ through $N-1$. Each edge is given as $(x_i, y_i)$, meaning that vertices $x_i$ and $y_i$ are connected by an edge.

Each vertex $i$ is assigned a value $a_i$. You want to add edges to the given forest so that it becomes a single connected graph. To add an edge, choose two different vertices $i$ and $j$ and place an edge between them. This operation costs $a_i + a_j$ dollars, and afterward neither vertex $i$ nor $j$ can be chosen again.

Find the minimum total cost needed to make the forest connected, or print "Impossible" if it is impossible.

Input is given in the following format:

$N$ $M$

$a_0$ $a_1$ $\ldots$ $a_{N-1}$

$x_1$ $y_1$

$\ldots$

$x_M$ $y_M$

Print the minimum total cost needed to make the forest connected, or print "Impossible" if it is impossible.

$1 \le N \le 100\,000$, $0 \le M \le N-1$, $1 \le a_i \le 10^9$, $0 \le x_i,y_i \le N-1$. The given graph is a forest. All input values are integers.

In Sample 1, connecting vertices $0$ and $5$ makes the graph connected, and the cost is $1 + 6 = 7$.

In Sample 2, the graph cannot be connected.

In Sample 3, the graph is connected whether or not we do anything.