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; 

vector<int> adj[100005];
#define ll long long 
ll val[100005]; 
ll n,m; 
ll ans=0; 

ll mi=1000000000000; 
int in; 
bool visited[100005]; 
ll dfs(int u,int p){
		visited[u]=1; 
		if(mi>val[u]){
				mi=val[u]; 
				in=u; 
		}
		for(int i=0;i<adj[u].size();i++){
				int v=adj[u][i]; 
				if(p==v) { continue; }
				else {
						dfs(v,u); 
				}
		}
}

		
int main(){
		cin>>n>>m; 
		for(int i=0;i<n;i++) { cin>>val[i]; }
		for(int i=0;i<m;i++) { int u,v; cin>>u>>v; adj[u].push_back(v); adj[v].push_back(u); }
		if(n==m+1) { cout<<0; return 0; }
		else if (n<2*(n-1-m)) { cout<<"Impossible"; return 0;  }
		set<int> bl; 
		int comp=0; 
		for(int i=0;i<n;i++) { 
				if(!visited[i]) {
						comp++; 
						mi=100000000000000; 
						dfs(i,-1); 
						ans+=mi; 
						bl.insert(in); 
				}
		}
		priority_queue<ll,vector<ll> , greater<ll> > q; 
		for(int i=0;i<n;i++){
				if(bl.find(i)==bl.end()){
						q.push(val[i]); 
				}
		}
		int req=2*(n-1-m)-comp; 
		while(req--){ ans+=q.top(); q.pop(); }
		cout<<ans; 
}


