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<iostream>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<vector>
#define FAST_IO ios::sync_with_stdio(false)
using namespace std;
int x,y,a[1000000],vis[100000],maxx,max1,n,m,cnt,maxt;
vector <int> E[123456];
long long ans;
void solve(int x)
{
	vis[x]=1;
	if (a[x]<maxx)
	  maxx=a[x],maxt=x;
   for(int i=0;i<E[x].size();i++){
        int u=E[x][i];
		if(!vis[u]) solve(u);
	}
	return;
}
int main()
{
	FAST_IO;
	cin>>n>>m;
	for (int i=1;i<=n;i++)
      cin>>a[i];
    if (n==1)
    {
	
      cout<<0<<endl;
      return 0;
}
    for (int i=1;i<=m;i++)
    {
	
      cin>>x>>y;
      x++;
      y++;
      E[x].push_back(y);
      E[y].push_back(x);
    }
   
    memset(vis,0,sizeof(vis));
    for (int i=1;i<=n;i++)
    {
    	maxx=2000000000;
    	maxt=0;
    	if (vis[i]==0)
         cnt++,solve(i),ans+=maxx; 
 
        
        a[maxt]=2000000001;
	}
	
	if (cnt*2-2>n) 
	{
	cout<<"Impossible";
	return 0;
    }
	sort(a+1,a+n+1);
	for (int i=1;i<=cnt-2;i++)
	{
		ans+=a[i];
	}
	cout<<ans;
	return 0;
}