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: Wrong Answer)

import java.io.*;
import java.util.*;

public class Main {
    FastScanner in;
    PrintWriter out;

    void solve() {
        int n = in.nextInt();
        int m = in.nextInt();
        O[] a = new O[n];
        for (int i = 0; i < n; i++) {
            a[i] = new O(i, in.nextInt());
        }
        Arrays.sort(a);
        p = new int[n];
        for (int i = 0; i < n; i++) {
            p[i] = i;
        }
        for (int i = 0; i < m; i++) {
            int fr = in.nextInt();
            int to = in.nextInt();
            unite(fr, to);
        }
        Queue<O> current = new ArrayDeque<>();
        long result = 0;
        for (O use : a) {
            if (current.size() == 0) {
                current.add(use);
                continue;
            }
            O last = current.peek();
            if (get(last.id) == get(use.id)) {
                current.add(use);
                continue;
            }
            current.poll();
            result += use.cost + last.cost;
            unite(last.id, use.id);
        }
        for (int i = 1; i < n; i++) {
            if (get(0) != get(i)) {
                out.println("Impossible");
                return;
            }
        }
        out.println(result);
    }

    int[] p;

    int get(int x) {
        return p[x] == x ? x : (p[x] = get(p[x]));
    }

    void unite(int x, int y) {
        p[get(x)] = get(y);
    }

    class O implements Comparable<O> {
        int id;
        int cost;

        public O(int id, int cost) {
            this.id = id;
            this.cost = cost;
        }

        @Override
        public int compareTo(O o) {
            return Integer.compare(cost, o.cost);
        }
    }

    void run() {
        try {
            in = new FastScanner(new File("Main.in"));
            out = new PrintWriter(new File("Main.out"));

            solve();

            out.close();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    void runIO() {

        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }

    public static void main(String[] args) {
        new Main().runIO();
    }
}