Problem:
Score : 600 points

Problem Statement

You are given a forest with N vertices and M edges. The vertices are numbered 0 through N-1.
The edges are given in the format (x_i,y_i), which means that Vertex x_i and y_i are connected by an edge.

Each vertex i has a value a_i.
You want to add edges in the given forest so that the forest becomes connected.
To add an edge, you choose two different vertices i and j, then span an edge between i and j.
This operation costs a_i + a_j dollars, and afterward neither Vertex i nor j can be selected again.

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

Constraints

1 ≤ N ≤ 100,000

0 ≤ M ≤ N-1

1 ≤ a_i ≤ 10^9

0 ≤ x_i,y_i ≤ N-1

The given graph is a forest.

All input values are integers.

Input

Input is given from Standard Input in the following format:

N M
a_0 a_1 .. a_{N-1}
x_1 y_1
x_2 y_2
:
x_M y_M

Output

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

Sample Input 1

7 5
1 2 3 4 5 6 7
3 0
4 0
1 2
1 3
5 6

Sample Output 1

7

If we connect vertices 0 and 5, the graph becomes connected, for the cost of 1 + 6 = 7 dollars.

Sample Input 2

5 0
3 1 4 1 5

Sample Output 2

Impossible

We can't make the graph connected.

Sample Input 3

1 0
5

Sample Output 3

0

The graph is already connected, so we do not need to add any edges.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        if ( m == n - 1) {
            System.out.println(0);
            return;
        }
        if (n < 2 * (n - m - 1)) {
            System.out.println("Impossible");
            return;
        }
        int[] weights = new int[n];
        ArrayList<LinkedList<Integer>> forest = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            weights[i] = sc.nextInt();
            forest.add(new LinkedList<Integer>());
        }
        for (int i = 0; i < m; i++) {
            int x = sc.nextInt();
            int y = sc.nextInt();
            forest.get(x).add(y);
            forest.get(y).add(x);
        }
        // DFS to find connected components
        long ans = 0;
        int count = 0;
        boolean[] visited = new boolean[n];
        PriorityQueue<Integer> remainCosts = new PriorityQueue<>();
        for (int i = 0; i < n; i++) {
            if (!visited[i]){
                List<Integer> costs = new ArrayList<>();
                Stack<Integer> stack = new Stack<Integer>();
                stack.push(i);
                while (!stack.isEmpty()) {
                    int vertex = stack.pop();
                    visited[vertex] = true;
                    costs.add(weights[vertex]);
                    LinkedList<Integer> edges = forest.get(vertex);
                    for (int edge : edges) {
                        if (!visited[edge]) {
                            stack.push(edge);
                        }
                    }
                }
                Collections.sort(costs);
                ans += costs.get(0);
                count++;
                for (int j = 1; j < costs.size(); j++) {
                    remainCosts.add(costs.get(j));
                }
            }
        }
        for (int i = count; i < 2 * (n - m - 1); i++) {
            ans += remainCosts.poll();
        }
        System.out.println(ans);
    }
}