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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef pair<int,int> pi;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<vector<int> > vvi;

int n,m;
int u,v;
pll a[100005];
ll x;
int visited[100005];
vvi f(100005);
int cnt;
int group(0);
int c[100005];
queue<pll> q;
map<pi,int> check;
ll newgroups[100005];

void dfs(int u)
{
    visited[u]=group;

    for(int i=0;i<f[u].size();++i)
    {
        int v = f[u][i];
        if(!visited[v]) dfs(v);
    }

}

int main()
{
    cin >> n >> m;
    for(ll i=0;i<n;++i) cin >> x,a[i].first=x,a[i].second=i;
    for(int i=0;i<m;++i)
    {
        cin >> u >> v;
        f[u].push_back(v);
        f[v].push_back(u);
    }
    sort(a,a+n);
    for(int i=0;i<n;++i)
    {
        if(!visited[i])
        {
            group=i+1;
            newgroups[group]=group;
            ++cnt;
            dfs(i);
        }
    }


        ll res(0);
        int edges = cnt-1;
        for(int i=0;i<n;++i)
        {
            if(!edges) break;
            if(q.empty())
            {
                q.push(a[i]);
            }
            else
            {
                pll fi = q.front();
                if(newgroups[visited[fi.second]] != newgroups[visited[a[i].second]] )
                {
                    newgroups[visited[fi.second]] = newgroups[visited[a[i].second]];
                    res += fi.first + a[i].first;
                    --edges;
                    q.pop();
                }
                else q.push(a[i]);
            }
        }
        if(edges==0) cout << res;
        else cout << "Impossible";


}

/*
4 1
1 2 3 4
0 1
*/