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>
#define F(i, l, r) for(int i = (l), _end_ = (int)(r); i <= _end_; ++i)
#define f(i, r, l) for(int i = (r), _end_ = (int)(l); i >= _end_; --i)
#define Set(a, v) memset(a, v, sizeof(a))
#define file(a) freopen(a".in","r",stdin),freopen(a".out","w",stdout)
using namespace std;

bool chkmin(int &a, int b) {return b < a ? a = b, 1 : 0;}
bool chkmax(int &a, int b) {return b > a ? a = b, 1 : 0;}

inline int read() {
 int x = 0, fh = 1; char ch = getchar();
    for (; !isdigit(ch); ch = getchar() ) if (ch == '-') fh = -1;
    for (; isdigit(ch); ch = getchar() ) x = (x<<1) + (x<<3) + (ch ^ '0');
    return x * fh;
}
int n,m;
int a[100005];
int vis[100005];
int cnt;
int fa[100005];
vector<int>e[100005];
int find(int x){return x==fa[x]?fa[x]:fa[x]=find(fa[x]);}
int main () {
    n=read();
	m=read();
	cnt=n;
	F(i,1,n)a[i]=read(),fa[i]=i;
	F(i,1,m){
	    int x=read(),y=read();
		x++;
		y++;
		 if(find(x)!=find(y))fa[find(x)]=find(y),cnt--;
	}
	if(cnt*2-2>n){
	  puts("Impossible");
	  return 0;
	}
	if(cnt==1){
	   puts("0");
	   return 0;
	}
	long long ans=0,tot=cnt*2-2;
	F(i,1,n){
	   e[find(i)].push_back(a[i]);
	}
	F(i,1,n){
	   if(e[i].size()){
	      sort(e[i].begin(),e[i].end());
		  ans+=e[i][0];
		  for(int j=1;j<e[i].size();j++)e[n+1].push_back(e[i][j]);
	       tot--;
	   }
	}
	sort(e[n+1].begin(),e[n+1].end());
	F(i,0,tot-1)ans+=e[n+1][i];
	printf("%lld\n",ans);
    return 0;
}