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;

typedef long long ll;

struct UF {
	vector<int> data;
	UF(int size) : data(size, -1) { }
	bool unite(int x, int y) {
		x = root(x); y = root(y);
		if (x != y) {
			if (data[y] < data[x]) swap(x, y);
			data[x] += data[y]; data[y] = x;
		}
		return x != y;
	}
	bool find(int x, int y) {
		return root(x) == root(y);
	}
	int root(int x) {
		return data[x] < 0 ? x : data[x] = root(data[x]);
	}
	int size(int x) {
		return -data[root(x)];
	}
};

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);

    int n,m;cin>>n>>m;
    vector<ll> a(n);
    UF uf(n);
    for(int i=0;i<n;i++) cin>>a[i];
    for(int i=0;i<m;i++){
      int x,y;cin>>x>>y;
      uf.unite(x,y);
    }
    if(m==n-1){
      cout<<0<<endl;
      return 0;
    }
    vector<priority_queue<ll,vector<ll>,greater<ll>>> qs(n);
    for(int i=0;i<n;i++){
      int par=uf.root(i);
      qs[par].push(a[i]);
    }
    bool f=true;
    ll res=0,cnt=0;
    priority_queue<ll,vector<ll>,greater<ll>> pq;
    for(int i=0;i<n;i++){
      if(qs[i].empty()) continue;
      cnt++;
      res += qs[i].top(); qs[i].pop();
      while(!qs[i].empty()){
        pq.push(qs[i].top()); qs[i].pop();
      }
    }
    for(int i=0;i<cnt-2;i++){
      if(pq.empty()){
        f=false;
        break;
      }
      res += pq.top();pq.pop();
    }
    if(!f){
      cout<<"Impossible"<<endl;
      return 0;
    }
    cout<<res<<endl;
}