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 {

    static class UnionFind {
        List<Integer> Parent;
        UnionFind(int N) {
            Parent = new ArrayList<Integer>();
            Integer[] values = new Integer[N];
            Arrays.fill(values, -1);
            Parent.addAll(Arrays.asList(values));
        }
        int root(int A) {
            if (Parent.get(A) < 0)
                return A;
            int root = root(Parent.get(A));
            Parent.set(A, root);
            return root;
        }
        int size(int A) {
            return -Parent.get(root(A));
        }

        boolean connect(int A, int B) {
            A = root(A);
            B = root(B);
            if (A == B) {
                return false;
            }

            if (size(A) < size(B)) {
                int temp = A;
                A = B;
                B = temp;
            }

            Parent.set(A, Parent.get(A) + Parent.get(B));
            Parent.set(B, A);

            return true;
        }
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        int[] a = new int[N];
        for (int i=0;i<N;i++) {
            a[i] = sc.nextInt();
        }
        UnionFind uf = new UnionFind(N);
        for (int i=0;i<M;i++) {
            int x = sc.nextInt();
            int y = sc.nextInt();
            uf.connect(x, y);
        }

        int[] root_tmp = new int[N];
        TreeSet<Integer> set = new TreeSet<Integer>();
        for (int i=0;i<N;i++) {
            root_tmp[i] = uf.root(i);
            set.add(root_tmp[i]);
        }
        ArrayList<Integer> list = new ArrayList<Integer>(set);
        if (list.size()==1) {
            System.out.println(0);
            return;
        }
        int[] root = new int[N];
        for (int i=0;i<N;i++) {
            root[i] = Collections.binarySearch(list, root_tmp[i]);
        }
        // System.out.println(Arrays.toString(root));

        ArrayList<ArrayList<Integer>> cost = new ArrayList<ArrayList<Integer>>();
        for (int i=0;i<list.size();i++) {
            ArrayList<Integer> add = new ArrayList<Integer>();
            cost.add(add);
        }

        for (int i=0;i<N;i++) {
            cost.get(root[i]).add(a[i]);
        }
        for (int i=0;i<list.size();i++) {
            Collections.sort(cost.get(i));
        }

        ArrayList<Integer> cost_1 = new ArrayList<Integer>();
        ArrayList<Integer> cost_2 = new ArrayList<Integer>();
        for (int i=0;i<list.size();i++) {
            cost_1.add(cost.get(i).get(0));
        }
        int cnt = 0;
        for (int i=0;i<list.size();i++) {
            if (cost.get(i).size()>1) {
                for (int j=1;j<cost.get(i).size();j++) {
                    cost_2.add(cost.get(i).get(j));
                }
            } else {
                cnt++;
                if (cnt>=3) {
                    // System.out.println("Impossible");
                    // return;
                }
            }
        }
        if ((N-1-M)*2>N) {
            System.out.println("Impossible");
            return;
        }

        long ans = 0L;
        for (int i=0;i<list.size();i++) {
            ans+=cost_1.get(i);
        }
        Collections.sort(cost_2);
        for (int i=0;i<list.size()-2;i++) {
            ans+=cost_2.get(i);
        }
        System.out.println(ans);
        // System.out.println(cost_1);
        // System.out.println(cost_2);
    }
}