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;
#define BUF (100005)
#define ll long long 
#define INF (1000000005)
int n,m;
int used[BUF];
int cnt;
ll ans;
ll cost[BUF];

vector<int> v[BUF];

ll m1cost;
int m1node;
ll m2cost;

ll treec1[BUF];
ll treen1[BUF];

vector<ll> cost2;

void dfs(int node){
	used[node]=1;
	if(m1cost>cost[node]){
		m1cost=cost[node];
		m1node = node;
	}
	for(auto x: v[node]){
		if(used[x]==0) dfs(x);
	}

	return;
}

int main(void){
	cin >> n >> m;
	for(int i=0;i<n;i++) cin >> cost[i];
	for(int i=1;i<=m;i++){
		int x,y;
		cin >> x >> y;
		v[x].push_back(y);
		v[y].push_back(x);
	}

	for(int i=0;i<n;i++){
		if(used[i]==0){
			m1cost=INF;
			dfs(i);
			treec1[cnt]=m1cost;
			treen1[cnt]=m1node;
			cnt++;
		}
	}

	if(cnt==1){
		cout << "0\n";
		return 0;
	}

	for(int i=0;i<cnt;i++){
		ans+=treec1[i];
	}

	for(int i=0;i<cnt;i++){
		cost[treen1[i]]=INF;
	}
	sort(cost,cost+n);
	for(int i=0;i<cnt-2;i++){
		if(cost[i]==INF){
			cout << "Impossible\n";
			return 0;
		}
		ans+=cost[i];
	}
	
	cout << ans << "\n";
	return 0;
}
