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.

Examples

Input

7 5
1 2 3 4 5 6 7
3 0
4 0
1 2
1 3
5 6


Output

7


Input

5 0
3 1 4 1 5


Output

Impossible


Input

1 0
5


Output

0
#include<bits/stdc++.h>
using namespace std;
int find(int x);
int same(int x,int y);
void unite(int x,int y);
priority_queue<int,vector<int>,greater<int> >pq[100009];
priority_queue<int,vector<int>,greater<int> >all;
int p[100009];

int main(){
  int n,m;
  int a[100009];
  cin>>n>>m;
  for(int i=0;i<n;i++){
    cin>>a[i];
    p[i]=i;
  }
  for(int i=0;i<m;i++){
    int x,y;
    cin>>x>>y;
    unite(x,y);
  }
  for(int i=0;i<n;i++){
    p[i]=find(p[i]);
    pq[p[i]].push(a[i]);
  }
  int cnt=0;
  long long ans=0;
  for(int i=0;i<n;i++){
    if(!pq[i].empty()){
      int now=pq[i].top();pq[i].pop();
      ans+=now;
      while(!pq[i].empty()){
        int t=pq[i].top();pq[i].pop();
        all.push(t);
      }
      cnt++;
    }
  }
  if(cnt==1){
    cout<<0<<endl;
    return(0);
  }
  for(int i=0;i<cnt-2;i++){
    if(all.empty()){
      cout<<"Impossible"<<endl;
      return(0);
    }
    int now=all.top();all.pop();
    ans+=now;
  }
  cout<<ans<<endl;
  return(0);
}

int find(int x){
  if(p[x]==x)return x;
  return p[x]=find(p[x]);
}

int same(int x,int y){
  if(find(x)==find(y))return 1;
  return 0;
}

void unite(int x,int y){
  x=find(x);
  y=find(y);
  p[x]=y;
}
