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.util.Arrays;
import java.util.HashMap;
import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.stream.IntStream;

class Main{

    static int[] uf;
    static int root(int v){
        if(uf[v]<0)return v;
        return uf[v]=root(uf[v]);
    }
    static int size(int v){
        return -uf[root(v)];
    }
    static void union(int u,int v){
        u = root(u);
        v = root(v);
        if(u==v)return;
        if(size(u)<size(v)){
            int tmp = u;
            u=v;
            v=tmp;
        }
        uf[u]+=uf[v];
        uf[v]=u;
    }
    static boolean same(int u,int v){
        return root(u)==root(v);
    }

    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int N = scan.nextInt();
        int M = scan.nextInt();
        class Node{
            int a,i;
            Node(int a,int i){
                this.a = a;
                this.i =i;
            }
        }
        int[] a = new int[N];
        for(int i=0;i<N;++i){
            a[i] = scan.nextInt();
        }

        uf = new int[N];
        Arrays.fill(uf,-1);

        while(M-->0){
            int x = scan.nextInt();
            int y = scan.nextInt();
            union(x,y);
        }

        Map<Integer, PriorityQueue<Integer> > queMap = new HashMap<>();
        for(int i=0;i<N;++i){
            if(!queMap.containsKey(root(i))){
                queMap.put(root(i), new PriorityQueue<>());
            }
                queMap.get(root(i)).add(a[i]);
        }
        List<Node> nodeList = new ArrayList<>();
        for(Map.Entry<Integer,PriorityQueue<Integer> > entry : queMap.entrySet()){
            nodeList.add(new Node(entry.getValue().size(), entry.getKey()));
        }
        nodeList.sort((x,y)->x.a - y.a);

        long res=0;
        while(nodeList.size()>1){
            for(int i=0;i<nodeList.size()-1-i;++i){
                int q1 = nodeList.get(i).i;
                int q2 = nodeList.get(nodeList.size()-1-i).i;

                if(queMap.get(q1).isEmpty() || queMap.get(q2).isEmpty()){
                    System.out.println("Impossible");
                    return;
                }

                res += (long)queMap.get(q1).poll() + queMap.get(q2).poll();
                while(!queMap.get(q1).isEmpty()){
                    queMap.get(q2).add(queMap.get(q1).poll());
                }
                queMap.remove(q1);
            }
            nodeList.clear();
            for(Map.Entry<Integer,PriorityQueue<Integer> > entry : queMap.entrySet()){
                nodeList.add(new Node(entry.getValue().size(), entry.getKey()));
            }
            nodeList.sort((x,y)->x.a - y.a);
        }
        System.out.println(res);


    }
}