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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define int long long
#define endl '\n'
#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define bug1( x ) {cerr << (#x) <<"="<< x << endl;}
#define bug2( x , y ) {cerr << (#x) <<"="<< (x) << "    " << (#y) << "="<< (y) << endl;}
#define bug3( x , y , z ) {cerr << (#x) <<"="<<(x) << "    " << (#y) <<"="<< (y) << "    " << (#z) <<"="<< (z) << endl;}
#define bug4( x , y , z , w) {cerr << (#x) <<"="<<(x) << "    " << (#y) <<"="<< (y) << "    " << (#z) <<"="<< (z) << "    " << (#w) <<"="<< w << endl;}
#define bug5( x , y , z , w ,p) {cerr << (#x) <<"="<<(x) << "    " << (#y) <<"="<< (y) << "    " << (#z) <<"="<< (z) << "    " << (#w) <<"="<< w << "    " << (#p) <<"="<< p << endl;}
#define bug6( x , y , z , w ,p , q) {cerr << (#x) <<"="<<(x) << "    " << (#y) <<"="<< (y) << "    " << (#z) <<"="<< (z) << "    " << (#w) <<"="<< w << "    " << (#p) <<"="<< p << "    " << (#q) <<"="<< q << endl;}
#define bugn( x , n ) {cerr << (#x) <<":";for(int i=0;i<n;i++)cerr << x[i] <<"  "; cerr << endl;}
#define bugnm( x , n , m ) {cerr << (#x)<<endl;for(int i=0;i<n;i++){cerr << "Row #" << i<< ":";for(int j=0;j<m;j++)cerr << x[i][j] << "   ";cerr << endl;}}
typedef long long ll;
typedef long double ld;
using namespace std;

//rank and path compression used
const int maxn = 1e5 + 5;
vector<int>par(maxn,-1),best(maxn),a(maxn);
int root(int v){return par[v] < 0 ? v : (par[v] = root(par[v]));}
void merge(int x,int y){	//	x and y are some tools (vertices)
        if((x = root(x)) == (y = root(y)) )    return ;
	if(par[y] < par[x])	// balancing the height of the tree
		swap(x, y);
	if( a[best[y]] < a[best[x]] ){
		best[x] = best[y];
	}
	par[x] += par[y];
	par[y] = x;
}

int32_t main(){
	IOS
	int n,m;cin>>n>>m;
	for(int i=0;i<n;i++){
		cin >> a[i];
		best[i] = i;
	}
	for(int i=0;i<m;i++){
		int u,v;cin>>u>>v;
		merge(u,v);
	}
	vector<int>used(n);
	int ans=0,cnt=0;
	for(int i=0;i<n;i++){
		if( root(i) == i ){
			used[ best[i] ] = 1;
			ans += a[best[i]];
			cnt++;
		}
	}
	if( cnt == 1){
		cout << 0 << endl; return 0;
	}
	if( 2 * ( cnt - 1) > n ){
		cout << "Impossible" << endl; return 0;
	}
	vector<int>lft;
	for(int i=0;i<n;i++){
		if( !used[i] ){
			lft.push_back(a[i]);
		}
	}
	sort(lft.begin(),lft.end());
	for(int i=0;i+cnt < 2*(cnt-1);i++){
		ans+=lft[i];
	}
	cout<<ans<<endl;
	
	
	
}
/*
 * long long or int?
 * index out of bound?
 * Tested on own test case?corner?
 * Make more general solution.
 * Read Read Read Read ....
 */