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,x;
int u,v;
int grp;

pll vv[100005];
vvi f(100005);
int visited[100005];
int groups[100005];
map<pll,int> check;

void dfs(int u)
{
    visited[u] = 1;
    groups[u] = grp;
    for(int i=0;i<f[u].size();++i)
    {
        if(!visited[f[u][i]]) dfs(f[u][i]);
    }
}

int root(int i)
{
    while(i!=groups[i]) groups[i]=groups[groups[i]],i=groups[i];
    return i;
}


int main()
{
    cin >> n >> m;
    for(int i=0;i<n;++i) cin >> x, vv[i].first = x,vv[i].second = i;
    sort(vv,vv+n);
    for(int i=0;i<m;++i)
    {
        cin >> u >> v;
        f[u].push_back(v);
        f[v].push_back(u);
    }

    int cnt(0);
    for(int i=0;i<n;++i)
    {
        if(!visited[i])
        {
            grp=i;
            groups[i]=i;
            cnt++;
            dfs(i);
        }
    }

    if(cnt > n/2 + 1) {cout << "Impossible";return 0;}


    queue<pll> q;
    int edges(cnt-1);
    ll res(0);
    for(int i=0;i<n;++i)
    {
        if(edges==0) break;
        if(q.empty()) q.push(vv[i]);
        else
        {
            pll b = q.front();
            //cout << b.first << " <===> " <<  vv[i].first << endl;
            //cout << root(visited[b.second]) << " ( " << visited[vv[i].second]<< " , " << root(visited[vv[i].second]) << endl;
            if(root(b.second)!=root(vv[i].second) && !check[pll(root(b.second),root(vv[i].second))] )
            {
                check[pll(root(b.second),root(vv[i].second))] = 1;
                check[pll(root(vv[i].second),root(b.second))] = 1;
                groups[root(vv[i].second)] = root(b.second);
                --edges;
                q.pop();
                res+= b.first + vv[i].first;
            }
            else q.push(vv[i]);
        }
    }
    if(edges) cout << "Impossible";
    else cout << res;
}

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