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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
long long F[200009],C[200009];
long long a[200009];
vector<long long> v[200009];
priority_queue<long long > q;
priority_queue<long long> p[200009];
void dfs(long long x, long long t)
{
    F[x] = 1;
    C[x] = t;
    for (long long i =0 ; i < v[x].size(); i++)
        if(F[v[x][i]]==0) dfs(v[x][i],t);
}
main()
{
    long long N,m;
    cin >> N >> m;
    for (long long i =0; i < N; i++)
    {
        cin >> a[i];
    }
    for (long long i =0; i < m; i++)
    {
        long long a,b;
        cin >> a >> b;
        v[a].push_back(b);
        v[b].push_back(a);
    }
    long long t =0;
    for (long long i =0; i < N; i++)
        if(F[i] ==0) {dfs(i,t); t++;}
    for (long long i =0; i < N; i++)
        p[C[i]].push(-a[i]);
        long long ans=0;
        if (m == N-1) {cout << 0 << endl; return 0;}
        m= 2*((N-1)-m);
    for (long long i =0; i < t; i++)
    {
        ans += p[i].top();
        p[i].pop();
        m --;
        while(p[i].size())
        {
            q.push(p[i].top());
            p[i].pop();
        }
    }
    if(q.size() < m) {cout <<"Impossible"<< endl; return 0;}
    while(m)
    {
        ans+=q.top();
        q.pop();
        m--;
    }
    cout << -ans << endl;

}